Difference: Pseudomanifold10Vertex (1 vs. 61)

Revision 612018-03-18 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 1623 to 1623
 
  10_9_0_0_0_0_0_0_1 2 265 12   1,[2]   a 10, #43      
  10_9_0_0_1_0_0_0_0 1 105737 6   0,[2]   a 9, #1      
  10_9_0_1_0_0_0_0_0 1 133745 6   Z Z a 8,N4      
Changed:
<
<
  10_10_0_0_0_0_0_0_0_a 0 177 10 Z Z Z     *    
>
>
  10_10_0_0_0_0_0_0_0_a 0 518 10 Z Z Z     *    
 
  10_10_0_0_0_0_0_0_0_b 0 615 10 Z 0,[2]       *    
  10_10_0_0_0_0_0_0_0_c 0 247882 0*     Z a,b 5 *    

Revision 602017-11-07 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 27 to 27
 
  • c - If Δ has 8 singular vertices and m of them are Klein bottles, then g2 ≥ 2 χ - 10 + (m/3)
  • d - If Δ has 8 singular vertices and any of them are real projective planes, then g2 ≥ 2 χ - 7
  • e - If Δ has 8 singular vertices including 3 projective planes and 2 Klein bottles, then g2 ≥ 2 χ - 5
Added:
>
>
  • f - Other
 

f-vector - A nonempty entry indicates that all possible f-vectors for complexes with the given singular vertices is known.

Line: 45 to 46
 

# Complex χ Triangulations minG2 H1 H2 H3 Γ f-vector ≅ delta epsilon 
<-- /editTable -->
Changed:
<
<
  10_0_0_0_0_0_0_0_10 20 5 15   19,[2]            
>
>
  10_0_0_0_0_0_0_0_10 20 5 15   19,[2]   f 10      
 
  10_0_0_0_0_0_0_0_6_0_4 22 1 15   21,[2]   a 10 *    
Changed:
<
<
  10_0_0_0_0_0_2_0_8 19 2 15   18,[2]     10      
>
>
  10_0_0_0_0_0_2_0_8 19 2 15   18,[2]            
 
  10_0_0_0_0_0_3_0_6_0_1 19 2 15   18,[2]   a 10      
  10_0_0_0_0_0_4_0_6 18 9 15   17,[2]            
  10_0_0_0_0_0_6_0_4 17 14 15   16,[2]            
Line: 55 to 56
 
  10_0_0_0_0_0_10_0_0 15 1 15   14,[2]       *    
  10_0_0_0_1_0_4_0_5 17 3 15   16,[2]            
  10_0_0_0_1_0_5_0_3_0_1 17 1 15   16,[2]   a 10 *    
Changed:
<
<
  10_0_0_0_1_0_6_0_3 16 29 15   15,[2]     10      
>
>
  10_0_0_0_1_0_6_0_3 16 29 15   15,[2]            
 
  10_0_0_0_1_0_7_0_1_0_1 16 1 15   15,[2]   a 10 *    
Changed:
<
<
  10_0_0_0_1_0_8_0_1 15 24 15   14,[2]     10      
>
>
  10_0_0_0_1_0_8_0_1 15 24 15   14,[2]            
 
  10_0_0_0_2_0_2_0_6 17 2 15   16,[2]            
  10_0_0_0_2_0_4_0_4 16 45 14   15,[2]            
  10_0_0_0_2_0_6_0_2 15 90 14   14,[2]            
Line: 300 to 301
 
  10_0_1_2_4_0_1_0_2 12 638 14   11,[2]            
  10_0_1_2_4_0_2_0_0_0_1 12 15 15   11,[2]   a 10      
  10_0_1_2_4_0_3_0_0 11 12360 13   10,[2]            
Changed:
<
<
  10_0_1_2_5_0_0_0_1_0_1 12 1 15   11,[2]   a 10

   
>
>
  10_0_1_2_5_0_0_0_1_0_1 12 1 15   11,[2]   a 10      
 
  10_0_1_2_5_0_1_0_1 11 2910 13   10,[2]            
  10_0_1_2_6_0_0_0_0_0_1 11 5 15   10,[2]   a 10      
  10_0_1_2_6_0_1_0_0 10 10053 12   9,[2]            

Revision 592017-09-05 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 1579 to 1579
 
  10_6_1_1_1_0_1_0_0 4 200588 10   3,[2]            
  10_6_1_2_0_0_1_0_0 4 4894 12   3,[2]            
  10_6_2_0_0_0_0_0_2 5 1054 13   4,[2]            
Changed:
<
<
  10_6_2_0_0_0_2_0_0 4 70076 10   3,[2]            
  10_6_2_0_0_0_1_0_0_0_1 5 67 15   4,[2]   a 10      
>
>
  10_6_2_0_0_0_2_0_0 4 70076 10   3,[2]            
  10_6_2_0_0_0_1_0_0_0_1 5 67 15   4,[2]   a 10      
 
  10_6_2_0_1_0_0_0_1 4 24763 12   3,[2]   a 10, #249      
  10_6_2_0_2_0_0_0_0 3 398219 9   2,[2]            
  10_6_2_1_0_0_0_0_1 4 10506 12   3,[2]   a 10, #204      

Revision 582017-08-28 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 27 to 27
 
  • c - If Δ has 8 singular vertices and m of them are Klein bottles, then g2 ≥ 2 χ - 10 + (m/3)
  • d - If Δ has 8 singular vertices and any of them are real projective planes, then g2 ≥ 2 χ - 7
  • e - If Δ has 8 singular vertices including 3 projective planes and 2 Klein bottles, then g2 ≥ 2 χ - 5
Deleted:
<
<
  • f - Combine a with the fact that if v and w are two vertices which do not share an edge, then g2(Δ) ≥ g2 (link v) + g2 (link w)
 

f-vector - A nonempty entry indicates that all possible f-vectors for complexes with the given singular vertices is known.

Line: 46 to 45
 

# Complex χ Triangulations minG2 H1 H2 H3 Γ f-vector ≅ delta epsilon 
<-- /editTable -->
Changed:
<
<
  10_0_0_0_0_0_0_0_10 20 5 15   19,[2]   f 10      
  10_0_0_0_0_0_0_0_6_0_4 22 1 15   21,[2]   a,f 10 *    
  10_0_0_0_0_0_2_0_8 19 2 15   18,[2]   f 10      
  10_0_0_0_0_0_3_0_6_0_1 19 2 15   18,[2]   a,f 10      
  10_0_0_0_0_0_4_0_6 18 9 15   17,[2]   f 10      
  10_0_0_0_0_0_6_0_4 17 14 15   16,[2]   f 10      
  10_0_0_0_0_0_8_0_2 16 9 15   15,[2]   f 10      
  10_0_0_0_0_0_10_0_0 15 1 15   14,[2]   f 10 *    
  10_0_0_0_1_0_4_0_5 17 3 15   16,[2]   f 10      
  10_0_0_0_1_0_5_0_3_0_1 17 1 15   16,[2]   a,f 10 *    
  10_0_0_0_1_0_6_0_3 16 29 15   15,[2]   f 10      
  10_0_0_0_1_0_7_0_1_0_1 16 1 15   15,[2]   a,f 10 *    
  10_0_0_0_1_0_8_0_1 15 24 15   14,[2]   f 10      
>
>
  10_0_0_0_0_0_0_0_10 20 5 15   19,[2]            
  10_0_0_0_0_0_0_0_6_0_4 22 1 15   21,[2]   a 10 *    
  10_0_0_0_0_0_2_0_8 19 2 15   18,[2]     10      
  10_0_0_0_0_0_3_0_6_0_1 19 2 15   18,[2]   a 10      
  10_0_0_0_0_0_4_0_6 18 9 15   17,[2]            
  10_0_0_0_0_0_6_0_4 17 14 15   16,[2]            
  10_0_0_0_0_0_8_0_2 16 9 15   15,[2]            
  10_0_0_0_0_0_10_0_0 15 1 15   14,[2]       *    
  10_0_0_0_1_0_4_0_5 17 3 15   16,[2]            
  10_0_0_0_1_0_5_0_3_0_1 17 1 15   16,[2]   a 10 *    
  10_0_0_0_1_0_6_0_3 16 29 15   15,[2]     10      
  10_0_0_0_1_0_7_0_1_0_1 16 1 15   15,[2]   a 10 *    
  10_0_0_0_1_0_8_0_1 15 24 15   14,[2]     10      
 
  10_0_0_0_2_0_2_0_6 17 2 15   16,[2]            
Changed:
<
<
  10_0_0_0_2_0_4_0_4 16 45 14   15,[2]   f        
  10_0_0_0_2_0_6_0_2 15 90 14   14,[2]   f        
  10_0_0_0_2_0_8_0_0 14 63 14   13,[2]   f        
>
>
  10_0_0_0_2_0_4_0_4 16 45 14   15,[2]            
  10_0_0_0_2_0_6_0_2 15 90 14   14,[2]            
  10_0_0_0_2_0_8_0_0 14 63 14   13,[2]            
 
  10_0_0_0_3_0_2_0_5 16 3 15   15,[2]            
  10_0_0_0_3_0_3_0_3_0_1 16 1 15   15,[2]   a 10 *    
  10_0_0_0_3_0_4_0_3 15 89 14   14,[2]            
Line: 79 to 78
 
  10_0_0_0_6_0_0_0_4 14 2 15   13,[2]            
  10_0_0_0_6_0_2_0_2 13 125 13   12,[2]            
  10_0_0_0_6_0_3_0_0_0_1 13 7 15   12,[2]   a 10      
Changed:
<
<
  10_0_0_0_6_0_4_0_0 12 675 12   11,[2]   f        
>
>
  10_0_0_0_6_0_4_0_0 12 675 12   11,[2]            
 
  10_0_0_0_7_0_0_0_3 13 13 14   12,[2]            
  10_0_0_0_7_0_1_0_1_0_1 13 4 15   12,[2]   a 10      
  10_0_0_0_7_0_2_0_1 12 243 14   11,[2]            
Line: 87 to 86
 
  10_0_0_0_8_0_2_0_0 11 876 13   10,[2]            
  10_0_0_0_9_0_0_0_1 11 38 14   10,[2]            
  10_0_0_0_10_0_0_0_0 10 43 14   9,[2]            
Changed:
<
<
  10_0_0_1_0_0_2_0_7 18 1 15   17,[2]   f 10 *    
  10_0_0_1_0_0_4_0_5 17 6 15   16,[2]   f 10      
  10_0_0_1_0_0_6_0_3 16 27 15   15,[2]   f 10      
  10_0_0_1_0_0_8_0_1 15 13 15   14,[2]   f 10      
>
>
  10_0_0_1_0_0_2_0_7 18 1 15   17,[2]       *    
  10_0_0_1_0_0_4_0_5 17 6 15   16,[2]            
  10_0_0_1_0_0_6_0_3 16 27 15   15,[2]            
  10_0_0_1_0_0_8_0_1 15 13 15   14,[2]            
 
  10_0_0_1_1_0_2_0_6 17 1 15   16,[2]       *    
  10_0_0_1_1_0_3_0_4_0_1 17 2 15   16,[2]   a 10      
Changed:
<
<
  10_0_0_1_1_0_4_0_4 16 52 14   15,[2]   f        
>
>
  10_0_0_1_1_0_4_0_4 16 52 14   15,[2]            
 
  10_0_0_1_1_0_5_0_2_0_1 16 2 15   15,[2]   a 10      
Changed:
<
<
  10_0_0_1_1_0_6_0_2 15 115 14   14,[2]   f        
>
>
  10_0_0_1_1_0_6_0_2 15 115 14   14,[2]            
 
  10_0_0_1_1_0_8_0_0 14 47 15   13,[2]            
  10_0_0_1_2_0_0_0_7 17 1 15   16,[2]       *    
  10_0_0_1_2_0_2_0_5 16 18 15   15,[2]            
Line: 125 to 124
 
  10_0_0_1_7_0_2_0_0 11 1411 14   10,[2]            
  10_0_0_1_8_0_0_0_1 11 63 14   10,[2]            
  10_0_0_1_9_0_0_0_0 10 67 14   9,[2]            
Changed:
<
<
  10_0_0_2_0_0_0_0_8 18 5 14   17,[2]   f        
>
>
  10_0_0_2_0_0_0_0_8 18 5 14   17,[2]            
 
  10_0_0_2_0_0_2_0_6 17 3 15   16,[2]            
Changed:
<
<
  10_0_0_2_0_0_4_0_4 16 26 14   15,[2]   f        
  10_0_0_2_0_0_6_0_2 15 44 14   14,[2]   f        
  10_0_0_2_0_0_8_0_0 14 24 14   13,[2]   f        
>
>
  10_0_0_2_0_0_4_0_4 16 26 14   15,[2]            
  10_0_0_2_0_0_6_0_2 15 44 14   14,[2]            
  10_0_0_2_0_0_8_0_0 14 24 14   13,[2]            
 
  10_0_0_2_1_0_2_0_5 16 16 15   15,[2]            
  10_0_0_2_1_0_4_0_3 15 73 15   14,[2]            
  10_0_0_2_1_0_6_0_1 14 194 14   13,[2]            
Line: 396 to 395
 
  10_0_2_2_0_0_2_0_4 14 11 14   13,[2]            
  10_0_2_2_0_0_3_0_2_0_1 14 1 15   13,[2]   a 10 *    
  10_0_2_2_0_0_4_0_2 13 101 13   12,[2]            
Changed:
<
<
  10_0_2_2_0_0_6_0_0 12 366 11   11,[2]   f        
>
>
  10_0_2_2_0_0_6_0_0 12 366 11   11,[2]            
 
  10_0_2_2_1_0_0_0_5 14 1 15   13,[2]       *    
  10_0_2_2_1_0_2_0_3 13 92 14   12,[2]            
  10_0_2_2_1_0_3_0_1_0_1 13 4 15   12,[2]   a 10      
Line: 661 to 660
 
  10_1_0_0_7_0_1_0_0_0_1 11 9 15   10,[2]   a 10      
  10_1_0_0_7_0_2_0_0 10 1586 11   9,[2]            
  10_1_0_0_8_0_0_0_1 10 86 13   9,[2]            
Changed:
<
<
  10_1_0_0_9_0_0_0_0 9 447 10   8,[2]   f 9      
>
>
  10_1_0_0_9_0_0_0_0 9 447 10   8,[2]            
 
  10_1_0_1_0_0_6_0_2 14 2 15   13,[2]            
  10_1_0_1_1_0_4_0_3 14 1 15   13,[2]       *    
  10_1_0_1_1_0_6_0_1 13 13 15   12,[2]            
Line: 680 to 679
 
  10_1_0_1_6_0_1_0_0_0_1 11 7 15   10,[2]   a 10      
  10_1_0_1_6_0_2_0_0 10 4184 12   9,[2]            
  10_1_0_1_7_0_0_0_1 10 232 13   9,[2]   a' 10, #1,β      
Changed:
<
<
  10_1_0_1_8_0_0_0_0 9 1743 10   8,[2]   f 9      
>
>
  10_1_0_1_8_0_0_0_0 9 1743 10   8,[2]            
 
  10_1_0_2_0_0_4_0_3 14 1 15   13,[2]       *    
  10_1_0_2_0_0_6_0_1 13 2 15   12,[2]            
  10_1_0_2_1_0_4_0_2 13 31 15   12,[2]            
Line: 716 to 715
 
  10_1_0_3_4_0_1_0_0_0_1 11 15 15   10,[2]   a 10      
  10_1_0_3_4_0_2_0_0 10 11726 11   9,[2]            
  10_1_0_3_5_0_0_0_1 10 776 12   9,[2]   a 10, #2      
Changed:
<
<
  10_1_0_3_6_0_0_0_0 9 5697 10   8,[2]   f 9      
>
>
  10_1_0_3_6_0_0_0_0 9 5697 10   8,[2]            
 
  10_1_0_4_0_0_0_0_5 14 3 15   13,[2]            
  10_1_0_4_0_0_2_0_3 13 1 15   12,[2]       *    
  10_1_0_4_0_0_4_0_1 12 83 13   11,[2]            
Line: 738 to 737
 
  10_1_0_5_2_0_1_0_0_0_1 11 1 15   10,[2]   a 10 *    
  10_1_0_5_2_0_2_0_0 10 2559 12   9,[2]            
  10_1_0_5_3_0_0_0_1 10 944 12   9,[2]   a 10, #4      
Changed:
<
<
  10_1_0_5_4_0_0_0_0 9 7808 10   8,[2]   f 9      
>
>
  10_1_0_5_4_0_0_0_0 9 7808 10   8,[2]            
 
  10_1_0_6_0_0_2_0_1 11 395 13   10,[2]            
  10_1_0_6_1_0_0_0_2 11 47 14   10,[2]            
  10_1_0_6_1_0_2_0_0 10 2213 11   9,[2]            
  10_1_0_6_2_0_0_0_1 10 88 14   9,[2]            
  10_1_0_6_3_0_0_0_0 9 263 11   8,[2]            
Changed:
<
<
  10_1_0_9_0_0_0_0_0 9 712 10   9,[] Z f 9      
>
>
  10_1_0_9_0_0_0_0_0 9 712 10   9,[] Z          
 
  10_1_1_0_1_0_7_0_0 12 6 15   11,[2]            
  10_1_1_0_2_0_5_0_1 12 58 14   11,[2]            
  10_1_1_0_3_0_3_0_2 12 97 14   11,[2]            
Line: 1269 to 1268
 
  10_2_6_2_0_0_0_0_0 5 27283 10   4,[2]            
  10_2_7_0_0_0_0_0_0_0_1 6 3 15   5,[2]   a 10      
  10_2_7_0_0_0_1_0_0 5 26373 10   4,[2]            
Changed:
<
<
  10_2_8_0_0_0_0_0_0 4 269194 6   3,[2]   f 8, N5      
>
>
  10_2_8_0_0_0_0_0_0 4 269194 6   3,[2]            
 
  10_3_0_0_3_0_4_0_0 9 27 14   8,[2]   b 10, #14      
  10_3_0_0_4_0_2_0_1 9 39 14   8,[2]   b 10, #25      
  10_3_0_0_5_0_0_0_2 9 2 15   8,[2]            

Revision 572017-08-26 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 60 to 60
 
  10_0_0_0_1_0_7_0_1_0_1 16 1 15   15,[2]   a,f 10 *    
  10_0_0_0_1_0_8_0_1 15 24 15   14,[2]   f 10      
  10_0_0_0_2_0_2_0_6 17 2 15   16,[2]            
Changed:
<
<
  10_0_0_0_2_0_4_0_4 16 45 14   15,[2]            
  10_0_0_0_2_0_6_0_2 15 90 14   14,[2]            
  10_0_0_0_2_0_8_0_0 14 63 14   13,[2]            
>
>
  10_0_0_0_2_0_4_0_4 16 45 14   15,[2]   f        
  10_0_0_0_2_0_6_0_2 15 90 14   14,[2]   f        
  10_0_0_0_2_0_8_0_0 14 63 14   13,[2]   f        
 
  10_0_0_0_3_0_2_0_5 16 3 15   15,[2]            
  10_0_0_0_3_0_3_0_3_0_1 16 1 15   15,[2]   a 10 *    
  10_0_0_0_3_0_4_0_3 15 89 14   14,[2]            
Line: 93 to 93
 
  10_0_0_1_0_0_8_0_1 15 13 15   14,[2]   f 10      
  10_0_0_1_1_0_2_0_6 17 1 15   16,[2]       *    
  10_0_0_1_1_0_3_0_4_0_1 17 2 15   16,[2]   a 10      
Changed:
<
<
  10_0_0_1_1_0_4_0_4 16 52 14   15,[2]            
>
>
  10_0_0_1_1_0_4_0_4 16 52 14   15,[2]   f        
 
  10_0_0_1_1_0_5_0_2_0_1 16 2 15   15,[2]   a 10      
Changed:
<
<
  10_0_0_1_1_0_6_0_2 15 115 14   14,[2]            
>
>
  10_0_0_1_1_0_6_0_2 15 115 14   14,[2]   f        
 
  10_0_0_1_1_0_8_0_0 14 47 15   13,[2]            
  10_0_0_1_2_0_0_0_7 17 1 15   16,[2]       *    
  10_0_0_1_2_0_2_0_5 16 18 15   15,[2]            
Line: 125 to 125
 
  10_0_0_1_7_0_2_0_0 11 1411 14   10,[2]            
  10_0_0_1_8_0_0_0_1 11 63 14   10,[2]            
  10_0_0_1_9_0_0_0_0 10 67 14   9,[2]            
Changed:
<
<
  10_0_0_2_0_0_0_0_8 18 5 14   17,[2]            
>
>
  10_0_0_2_0_0_0_0_8 18 5 14   17,[2]   f        
 
  10_0_0_2_0_0_2_0_6 17 3 15   16,[2]            
Changed:
<
<
  10_0_0_2_0_0_4_0_4 16 26 14   15,[2]            
  10_0_0_2_0_0_6_0_2 15 44 14   14,[2]            
  10_0_0_2_0_0_8_0_0 14 24 14   13,[2]            
>
>
  10_0_0_2_0_0_4_0_4 16 26 14   15,[2]   f        
  10_0_0_2_0_0_6_0_2 15 44 14   14,[2]   f        
  10_0_0_2_0_0_8_0_0 14 24 14   13,[2]   f        
 
  10_0_0_2_1_0_2_0_5 16 16 15   15,[2]            
  10_0_0_2_1_0_4_0_3 15 73 15   14,[2]            
  10_0_0_2_1_0_6_0_1 14 194 14   13,[2]            
Line: 396 to 396
 
  10_0_2_2_0_0_2_0_4 14 11 14   13,[2]            
  10_0_2_2_0_0_3_0_2_0_1 14 1 15   13,[2]   a 10 *    
  10_0_2_2_0_0_4_0_2 13 101 13   12,[2]            
Changed:
<
<
  10_0_2_2_0_0_6_0_0 12 366 11   11,[2]            
>
>
  10_0_2_2_0_0_6_0_0 12 366 11   11,[2]   f        
 
  10_0_2_2_1_0_0_0_5 14 1 15   13,[2]       *    
  10_0_2_2_1_0_2_0_3 13 92 14   12,[2]            
  10_0_2_2_1_0_3_0_1_0_1 13 4 15   12,[2]   a 10      

Revision 562017-08-25 - EdwardSwartz

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META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 53 to 53
 
  10_0_0_0_0_0_4_0_6 18 9 15   17,[2]   f 10      
  10_0_0_0_0_0_6_0_4 17 14 15   16,[2]   f 10      
  10_0_0_0_0_0_8_0_2 16 9 15   15,[2]   f 10      
Changed:
<
<
  10_0_0_0_0_0_10_0_0 15 1 15   14,[2]   f   *    
>
>
  10_0_0_0_0_0_10_0_0 15 1 15   14,[2]   f 10 *    
 
  10_0_0_0_1_0_4_0_5 17 3 15   16,[2]   f 10      
  10_0_0_0_1_0_5_0_3_0_1 17 1 15   16,[2]   a,f 10 *    
  10_0_0_0_1_0_6_0_3 16 29 15   15,[2]   f 10      

Revision 552017-08-24 - EdwardSwartz

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META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 661 to 661
 
  10_1_0_0_7_0_1_0_0_0_1 11 9 15   10,[2]   a 10      
  10_1_0_0_7_0_2_0_0 10 1586 11   9,[2]            
  10_1_0_0_8_0_0_0_1 10 86 13   9,[2]            
Changed:
<
<
  10_1_0_0_9_0_0_0_0 9 447 10   8,[2]   f        
>
>
  10_1_0_0_9_0_0_0_0 9 447 10   8,[2]   f 9      
 
  10_1_0_1_0_0_6_0_2 14 2 15   13,[2]            
  10_1_0_1_1_0_4_0_3 14 1 15   13,[2]       *    
  10_1_0_1_1_0_6_0_1 13 13 15   12,[2]            
Line: 680 to 680
 
  10_1_0_1_6_0_1_0_0_0_1 11 7 15   10,[2]   a 10      
  10_1_0_1_6_0_2_0_0 10 4184 12   9,[2]            
  10_1_0_1_7_0_0_0_1 10 232 13   9,[2]   a' 10, #1,β      
Changed:
<
<
  10_1_0_1_8_0_0_0_0 9 1743 10   8,[2]   f        
>
>
  10_1_0_1_8_0_0_0_0 9 1743 10   8,[2]   f 9      
 
  10_1_0_2_0_0_4_0_3 14 1 15   13,[2]       *    
  10_1_0_2_0_0_6_0_1 13 2 15   12,[2]            
  10_1_0_2_1_0_4_0_2 13 31 15   12,[2]            
Line: 716 to 716
 
  10_1_0_3_4_0_1_0_0_0_1 11 15 15   10,[2]   a 10      
  10_1_0_3_4_0_2_0_0 10 11726 11   9,[2]            
  10_1_0_3_5_0_0_0_1 10 776 12   9,[2]   a 10, #2      
Changed:
<
<
  10_1_0_3_6_0_0_0_0 9 5697 10   8,[2]   f        
>
>
  10_1_0_3_6_0_0_0_0 9 5697 10   8,[2]   f 9      
 
  10_1_0_4_0_0_0_0_5 14 3 15   13,[2]            
  10_1_0_4_0_0_2_0_3 13 1 15   12,[2]       *    
  10_1_0_4_0_0_4_0_1 12 83 13   11,[2]            
Line: 738 to 738
 
  10_1_0_5_2_0_1_0_0_0_1 11 1 15   10,[2]   a 10 *    
  10_1_0_5_2_0_2_0_0 10 2559 12   9,[2]            
  10_1_0_5_3_0_0_0_1 10 944 12   9,[2]   a 10, #4      
Changed:
<
<
  10_1_0_5_4_0_0_0_0 9 7808 10   8,[2]   f        
>
>
  10_1_0_5_4_0_0_0_0 9 7808 10   8,[2]   f 9      
 
  10_1_0_6_0_0_2_0_1 11 395 13   10,[2]            
  10_1_0_6_1_0_0_0_2 11 47 14   10,[2]            
  10_1_0_6_1_0_2_0_0 10 2213 11   9,[2]            
  10_1_0_6_2_0_0_0_1 10 88 14   9,[2]            
  10_1_0_6_3_0_0_0_0 9 263 11   8,[2]            
Changed:
<
<
  10_1_0_9_0_0_0_0_0 9 712 10   9,[] Z f        
>
>
  10_1_0_9_0_0_0_0_0 9 712 10   9,[] Z f 9      
 
  10_1_1_0_1_0_7_0_0 12 6 15   11,[2]            
  10_1_1_0_2_0_5_0_1 12 58 14   11,[2]            
  10_1_1_0_3_0_3_0_2 12 97 14   11,[2]            

Revision 542017-08-24 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 22 to 22
 

H1, H2, H3 - Integer homology groups of all of the triangulations with the given vertex links on 10 vertices. The homology group is trivial if blank. For H2 the shorthand n,[2] stands for the direct sum of Z/2Z and the free abelian group of rank n.

Γ - Γ is the minimum of g2 over all triangulations of a three-dimensional normal pseudomanifold with the given singular vertices. A letter in this column indicates that minG2=Γ and the proof is indicated below. A superscript ' indicates that Γ=minG2-1 and 11 vertices are needed to realize Γ.

Changed:
<
<
  • a - For any vertex v of Δ, g2(Δ) ≥ g2 (link v).
>
>
  • a - For any subcomplex Δ' of Δ, g2(Δ) ≥ g2 (Δ'). Usually v is a vertex and Δ'=st(v), so g2(Δ) ≥ g2 (st v) = g2 (link v).
 
  • b - If n is the number of singular vertices, then g2 ≥ 2 χ - ( n-3 choose 3). If n-3 < 3, then the binomial coefficient is interepreted as zero.
  • c - If Δ has 8 singular vertices and m of them are Klein bottles, then g2 ≥ 2 χ - 10 + (m/3)
  • d - If Δ has 8 singular vertices and any of them are real projective planes, then g2 ≥ 2 χ - 7
  • e - If Δ has 8 singular vertices including 3 projective planes and 2 Klein bottles, then g2 ≥ 2 χ - 5
Changed:
<
<
  • f - a and if v and w are two vertices which do not share an edge, then g2(Δ) ≥ g2 (link v) + g2 (link w)
>
>
  • f - Combine a with the fact that if v and w are two vertices which do not share an edge, then g2(Δ) ≥ g2 (link v) + g2 (link w)
 

f-vector - A nonempty entry indicates that all possible f-vectors for complexes with the given singular vertices is known.

Line: 46 to 46
 

# Complex χ Triangulations minG2 H1 H2 H3 Γ f-vector ≅ delta epsilon 
<-- /editTable -->
Changed:
<
<
  10_0_0_0_0_0_0_0_10 20 5 15   19,[2]            
  10_0_0_0_0_0_0_0_6_0_4 22 1 15   21,[2]   a 10 *    
  10_0_0_0_0_0_2_0_8 19 2 15   18,[2]            
  10_0_0_0_0_0_3_0_6_0_1 19 2 15   18,[2]   a 10      
  10_0_0_0_0_0_4_0_6 18 9 15   17,[2]            
  10_0_0_0_0_0_6_0_4 17 14 15   16,[2]            
  10_0_0_0_0_0_8_0_2 16 9 15   15,[2]            
  10_0_0_0_0_0_10_0_0 15 1 15   14,[2]       *    
  10_0_0_0_1_0_4_0_5 17 3 15   16,[2]            
  10_0_0_0_1_0_5_0_3_0_1 17 1 15   16,[2]   a 10 *    
  10_0_0_0_1_0_6_0_3 16 29 15   15,[2]            
  10_0_0_0_1_0_7_0_1_0_1 16 1 15   15,[2]   a 10 *    
  10_0_0_0_1_0_8_0_1 15 24 15   14,[2]            
>
>
  10_0_0_0_0_0_0_0_10 20 5 15   19,[2]   f 10      
  10_0_0_0_0_0_0_0_6_0_4 22 1 15   21,[2]   a,f 10 *    
  10_0_0_0_0_0_2_0_8 19 2 15   18,[2]   f 10      
  10_0_0_0_0_0_3_0_6_0_1 19 2 15   18,[2]   a,f 10      
  10_0_0_0_0_0_4_0_6 18 9 15   17,[2]   f 10      
  10_0_0_0_0_0_6_0_4 17 14 15   16,[2]   f 10      
  10_0_0_0_0_0_8_0_2 16 9 15   15,[2]   f 10      
  10_0_0_0_0_0_10_0_0 15 1 15   14,[2]   f   *    
  10_0_0_0_1_0_4_0_5 17 3 15   16,[2]   f 10      
  10_0_0_0_1_0_5_0_3_0_1 17 1 15   16,[2]   a,f 10 *    
  10_0_0_0_1_0_6_0_3 16 29 15   15,[2]   f 10      
  10_0_0_0_1_0_7_0_1_0_1 16 1 15   15,[2]   a,f 10 *    
  10_0_0_0_1_0_8_0_1 15 24 15   14,[2]   f 10      
 
  10_0_0_0_2_0_2_0_6 17 2 15   16,[2]            
  10_0_0_0_2_0_4_0_4 16 45 14   15,[2]            
  10_0_0_0_2_0_6_0_2 15 90 14   14,[2]            
Line: 79 to 79
 
  10_0_0_0_6_0_0_0_4 14 2 15   13,[2]            
  10_0_0_0_6_0_2_0_2 13 125 13   12,[2]            
  10_0_0_0_6_0_3_0_0_0_1 13 7 15   12,[2]   a 10      
Changed:
<
<
  10_0_0_0_6_0_4_0_0 12 675 12   11,[2]            
>
>
  10_0_0_0_6_0_4_0_0 12 675 12   11,[2]   f        
 
  10_0_0_0_7_0_0_0_3 13 13 14   12,[2]            
  10_0_0_0_7_0_1_0_1_0_1 13 4 15   12,[2]   a 10      
  10_0_0_0_7_0_2_0_1 12 243 14   11,[2]            
Line: 87 to 87
 
  10_0_0_0_8_0_2_0_0 11 876 13   10,[2]            
  10_0_0_0_9_0_0_0_1 11 38 14   10,[2]            
  10_0_0_0_10_0_0_0_0 10 43 14   9,[2]            
Changed:
<
<
  10_0_0_1_0_0_2_0_7 18 1 15   17,[2]       *    
  10_0_0_1_0_0_4_0_5 17 6 15   16,[2]            
  10_0_0_1_0_0_6_0_3 16 27 15   15,[2]            
  10_0_0_1_0_0_8_0_1 15 13 15   14,[2]            
>
>
  10_0_0_1_0_0_2_0_7 18 1 15   17,[2]   f 10 *    
  10_0_0_1_0_0_4_0_5 17 6 15   16,[2]   f 10      
  10_0_0_1_0_0_6_0_3 16 27 15   15,[2]   f 10      
  10_0_0_1_0_0_8_0_1 15 13 15   14,[2]   f 10      
 
  10_0_0_1_1_0_2_0_6 17 1 15   16,[2]       *    
  10_0_0_1_1_0_3_0_4_0_1 17 2 15   16,[2]   a 10      
  10_0_0_1_1_0_4_0_4 16 52 14   15,[2]            
Line: 661 to 661
 
  10_1_0_0_7_0_1_0_0_0_1 11 9 15   10,[2]   a 10      
  10_1_0_0_7_0_2_0_0 10 1586 11   9,[2]            
  10_1_0_0_8_0_0_0_1 10 86 13   9,[2]            
Changed:
<
<
  10_1_0_0_9_0_0_0_0 9 447 10   8,[2]            
>
>
  10_1_0_0_9_0_0_0_0 9 447 10   8,[2]   f        
 
  10_1_0_1_0_0_6_0_2 14 2 15   13,[2]            
  10_1_0_1_1_0_4_0_3 14 1 15   13,[2]       *    
  10_1_0_1_1_0_6_0_1 13 13 15   12,[2]            
Line: 680 to 680
 
  10_1_0_1_6_0_1_0_0_0_1 11 7 15   10,[2]   a 10      
  10_1_0_1_6_0_2_0_0 10 4184 12   9,[2]            
  10_1_0_1_7_0_0_0_1 10 232 13   9,[2]   a' 10, #1,β      
Changed:
<
<
  10_1_0_1_8_0_0_0_0 9 1743 10   8,[2]            
>
>
  10_1_0_1_8_0_0_0_0 9 1743 10   8,[2]   f        
 
  10_1_0_2_0_0_4_0_3 14 1 15   13,[2]       *    
  10_1_0_2_0_0_6_0_1 13 2 15   12,[2]            
  10_1_0_2_1_0_4_0_2 13 31 15   12,[2]            
Line: 716 to 716
 
  10_1_0_3_4_0_1_0_0_0_1 11 15 15   10,[2]   a 10      
  10_1_0_3_4_0_2_0_0 10 11726 11   9,[2]            
  10_1_0_3_5_0_0_0_1 10 776 12   9,[2]   a 10, #2      
Changed:
<
<
  10_1_0_3_6_0_0_0_0 9 5697 10   8,[2]            
>
>
  10_1_0_3_6_0_0_0_0 9 5697 10   8,[2]   f        
 
  10_1_0_4_0_0_0_0_5 14 3 15   13,[2]            
  10_1_0_4_0_0_2_0_3 13 1 15   12,[2]       *    
  10_1_0_4_0_0_4_0_1 12 83 13   11,[2]            
Line: 738 to 738
 
  10_1_0_5_2_0_1_0_0_0_1 11 1 15   10,[2]   a 10 *    
  10_1_0_5_2_0_2_0_0 10 2559 12   9,[2]            
  10_1_0_5_3_0_0_0_1 10 944 12   9,[2]   a 10, #4      
Changed:
<
<
  10_1_0_5_4_0_0_0_0 9 7808 10   8,[2]            
>
>
  10_1_0_5_4_0_0_0_0 9 7808 10   8,[2]   f        
 
  10_1_0_6_0_0_2_0_1 11 395 13   10,[2]            
  10_1_0_6_1_0_0_0_2 11 47 14   10,[2]            
  10_1_0_6_1_0_2_0_0 10 2213 11   9,[2]            
  10_1_0_6_2_0_0_0_1 10 88 14   9,[2]            
  10_1_0_6_3_0_0_0_0 9 263 11   8,[2]            
Changed:
<
<
  10_1_0_9_0_0_0_0_0 9 712 10   9,[] Z          
>
>
  10_1_0_9_0_0_0_0_0 9 712 10   9,[] Z f        
 
  10_1_1_0_1_0_7_0_0 12 6 15   11,[2]            
  10_1_1_0_2_0_5_0_1 12 58 14   11,[2]            
  10_1_1_0_3_0_3_0_2 12 97 14   11,[2]            

Revision 532017-08-19 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 27 to 27
 
  • c - If Δ has 8 singular vertices and m of them are Klein bottles, then g2 ≥ 2 χ - 10 + (m/3)
  • d - If Δ has 8 singular vertices and any of them are real projective planes, then g2 ≥ 2 χ - 7
  • e - If Δ has 8 singular vertices including 3 projective planes and 2 Klein bottles, then g2 ≥ 2 χ - 5
Added:
>
>
  • f - a and if v and w are two vertices which do not share an edge, then g2(Δ) ≥ g2 (link v) + g2 (link w)
 

f-vector - A nonempty entry indicates that all possible f-vectors for complexes with the given singular vertices is known.

Line: 1268 to 1269
 
  10_2_6_2_0_0_0_0_0 5 27283 10   4,[2]            
  10_2_7_0_0_0_0_0_0_0_1 6 3 15   5,[2]   a 10      
  10_2_7_0_0_0_1_0_0 5 26373 10   4,[2]            
Changed:
<
<
  10_2_8_0_0_0_0_0_0 4 269194 6   3,[2]            
>
>
  10_2_8_0_0_0_0_0_0 4 269194 6   3,[2]   f 8, N5      
 
  10_3_0_0_3_0_4_0_0 9 27 14   8,[2]   b 10, #14      
  10_3_0_0_4_0_2_0_1 9 39 14   8,[2]   b 10, #25      
  10_3_0_0_5_0_0_0_2 9 2 15   8,[2]            

Revision 522017-08-18 - EdwardSwartz

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META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 935 to 935
 
  10_1_3_3_1_0_0_0_1_0_1 10 1 15   9,[2]   a 10 *    
  10_1_3_3_1_0_1_0_1 9 6406 12   8,[2]   a 10, #48      
  10_1_3_3_2_0_0_0_0_0_1 9 12 15   8,[2]   a 10      
Changed:
<
<
  10_1_3_3_2_0_1_0_0 8 72805 9   7,[2]   a        
>
>
  10_1_3_3_2_0_1_0_0 8 72805 9   7,[2]   a 10, #23      
 
  10_1_3_4_0_0_0_0_1_0_1 10 8 15   9,[2]   a 10      
  10_1_3_4_0_0_1_0_1 9 228 13   8,[2]            
  10_1_3_4_1_0_0_0_0_0_1 9 2 15   8,[2]   a 10      
Line: 988 to 988
 
  10_1_5_0_2_0_0_0_1_0_1 9 6 15   8,[2]   a 10      
  10_1_5_0_2_0_1_0_1 8 10866 12   7,[2]   a 10, #43      
  10_1_5_0_3_0_0_0_0_0_1 8 4 15   7,[2]   a 10      
Changed:
<
<
  10_1_5_0_3_0_1_0_0 7 126921 9   6,[2]   a        
>
>
  10_1_5_0_3_0_1_0_0 7 126921 9   6,[2]   a 10, #42      
 
  10_1_5_1_0_0_1_0_2 9 108 14   8,[2]            
  10_1_5_1_0_0_3_0_0 8 4900 12   7,[2]            
  10_1_5_1_1_0_1_0_1 8 8881 12   7,[2]   a 10, #41      
Line: 1402 to 1402
 
  10_3_5_0_0_0_0_0_1_0_1 7 8 15   6,[2]   a 10      
  10_3_5_0_0_0_1_0_1 6 8883 12   5,[2]   a 10, #225      
  10_3_5_0_1_0_0_0_0_0_1 6 15 15   5,[2]   a 10      
Changed:
<
<
  10_3_5_0_1_0_1_0_0 5 246321 9   4,[2]   a        
>
>
  10_3_5_0_1_0_1_0_0 5 246321 9   4,[2]   a 10, #174      
 
  10_3_5_1_0_0_0_0_0_0_1 6 8 15   5,[2]   a 10      
  10_3_5_1_0_0_1_0_0 5 155420 10   4,[2]            
  10_3_6_0_0_0_0_0_1 5 4864 12   4,[2]   a 10, #239      
Line: 1497 to 1497
 
  10_4_4_1_1_0_0_0_0 4 421809 9   3,[2]            
  10_4_4_2_0_0_0_0_0 4 371357 8   3,[2]            
  10_4_5_0_0_0_0_0_0_0_1 5 12 15   3,[2]   a 10      
Changed:
<
<
  10_4_5_0_0_0_1_0_0 4 252067 9   4,[2]   a        
>
>
  10_4_5_0_0_0_1_0_0 4 252067 9   4,[2]   a 10, #34463      
 
  10_4_6_0_0_0_0_0_0 3 19454 9   2,[2]            
  10_5_0_0_1_0_4_0_0 7 68 14   6,[2]   b 10, #10      
  10_5_0_0_2_0_2_0_1 7 71 14   6,[2]   b 10, #30      
Line: 1549 to 1549
 
  10_5_2_3_0_0_0_0_0 4 473 12   3,[2]            
  10_5_3_0_0_0_1_0_1 5 13149 12   4,[2]   a 10, #274      
  10_5_3_0_1_0_0_0_0_0_1 5 94 15   4,[2]   a 10      
Changed:
<
<
  10_5_3_0_1_0_1_0_0 4 646350 9   3,[2]   a        
>
>
  10_5_3_0_1_0_1_0_0 4 646350 9   3,[2]   a 10, 587417      
 
  10_5_3_1_0_0_0_0_0_0_1 5 43 15   4,[2]   a 10      
  10_5_3_1_0_0_1_0_0 4 258534 10   3,[2]            
  10_5_4_0_0_0_0_0_1 4 12477 12   3,[2]   a 10, #293      

Revision 512017-08-14 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 1094 to 1094
 
  10_2_1_0_2_0_3_0_2 11 3 15   10,[2]   d 10      
  10_2_1_0_2_0_5_0_0 10 75 14   9,[2]            
  10_2_1_0_3_0_1_0_3 11 1 15   10,[2]   d 10 *    
Changed:
<
<
  10_2_1_0_3_0_3_0_1 10 355 14   9,[2]            
>
>
  10_2_1_0_3_0_3_0_1 10 355 14   9,[2]   d' 10, #24, β      
 
  10_2_1_0_4_0_1_0_2 10 109 14   9,[2]            
  10_2_1_0_4_0_2_0_0_0_1 10 21 15   9,[2]   a 10      
  10_2_1_0_4_0_3_0_0 9 4099 12   8,[2]            
Line: 1105 to 1105
 
  10_2_1_1_1_0_4_0_0_0_1 11 1 15   10,[2]   a,d 10 *    
  10_2_1_1_1_0_5_0_0 10 92 14   9,[2]   d' 10,#3,β      
  10_2_1_1_2_0_1_0_3 11 2 15   10,[2]   d 10      
Changed:
<
<
  10_2_1_1_2_0_3_0_1 10 421 14   9,[2]            
>
>
  10_2_1_1_2_0_3_0_1 10 421 14   9,[2]   d' 10,#39, β      
 
  10_2_1_1_3_0_1_0_2 10 232 14   9,[2]            
  10_2_1_1_3_0_2_0_0_0_1 10 11 15   9,[2]   a 10      
Changed:
<
<
  10_2_1_1_3_0_3_0_0 9 9136 12   8,[2]            
>
>
  10_2_1_1_3_0_3_0_0 9 9136 12   8,[2]   d' 10, #11, β      
 
  10_2_1_1_4_0_1_0_1 9 5008 12   8,[2]   a 10, #18      
  10_2_1_1_5_0_0_0_0_0_1 9 11 15   8,[2]   a 10      
  10_2_1_1_5_0_1_0_0 8 29384 11   7,[2]            
  10_2_1_2_0_0_3_0_2 11 4 15   10,[2]   d 10      
Changed:
<
<
  10_2_1_2_0_0_5_0_0 10 68 14   9,[2]            
>
>
  10_2_1_2_0_0_5_0_0 10 68 14   9,[2]   d' 10, #2, β      
 
  10_2_1_2_1_0_1_0_3 11 8 15   10,[2]   d 10      
  10_2_1_2_1_0_3_0_1 10 529 13   9,[2]   d 10, #1      
  10_2_1_2_2_0_1_0_2 10 217 14   9,[2]            

Revision 502017-08-13 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 678 to 678
 
  10_1_0_1_6_0_0_0_2 11 112 12   10,[2]   a 10, #1      
  10_1_0_1_6_0_1_0_0_0_1 11 7 15   10,[2]   a 10      
  10_1_0_1_6_0_2_0_0 10 4184 12   9,[2]            
Changed:
<
<
  10_1_0_1_7_0_0_0_1 10 232 13   9,[2]            
>
>
  10_1_0_1_7_0_0_0_1 10 232 13   9,[2]   a' 10, #1,β      
 
  10_1_0_1_8_0_0_0_0 9 1743 10   8,[2]            
  10_1_0_2_0_0_4_0_3 14 1 15   13,[2]       *    
  10_1_0_2_0_0_6_0_1 13 2 15   12,[2]            
Line: 698 to 698
 
  10_1_0_2_5_0_0_0_2 11 118 14   10,[2]            
  10_1_0_2_5_0_1_0_0_0_1 11 4 15   10,[2]   a 10      
  10_1_0_2_5_0_2_0_0 10 9413 11   9,[2]            
Changed:
<
<
  10_1_0_2_6_0_0_0_1 10 699 13   9,[2]            
>
>
  10_1_0_2_6_0_0_0_1 10 699 13   9,[2]   a' 10, #1, β      
 
  10_1_0_2_7_0_0_0_0 9 2967 11   8,[2]            
  10_1_0_3_0_0_4_0_2 13 18 14   12,[2]            
  10_1_0_3_0_0_6_0_0 12 23 14   11,[2]            
Line: 728 to 728
 
  10_1_0_4_3_0_0_0_2 11 61 14   10,[2]            
  10_1_0_4_3_0_1_0_0_0_1 11 27 15   10,[2]   a 10      
  10_1_0_4_3_0_2_0_0 10 7136 11   9,[2]            
Changed:
<
<
  10_1_0_4_4_0_0_0_1 10 623 13   9,[2]            
>
>
  10_1_0_4_4_0_0_0_1 10 623 13   9,[2]   a' 10, #3, β      
 
  10_1_0_4_5_0_0_0_0 9 1005 11   8,[2]            
  10_1_0_5_0_0_2_0_2 12 14 15   11,[2]            
  10_1_0_5_0_0_4_0_0 11 525 11   10,[2]            
Line: 864 to 864
 
  10_1_2_2_1_0_4_0_0 10 4424 11   9,[2]            
  10_1_2_2_2_0_0_0_3 11 34 14   10,[2]            
  10_1_2_2_2_0_1_0_1_0_1 11 14 15   10,[2]   a 10      
Changed:
<
<
  10_1_2_2_2_0_2_0_1 10 6638 13   9,[2]            
>
>
  10_1_2_2_2_0_2_0_1 10 6638 13   9,[2]   a' 10, #443,β      
 
  10_1_2_2_3_0_0_0_2 10 1105 13   9,[2]            
  10_1_2_2_3_0_1_0_0_0_1 10 68 15   9,[2]   a 10      
  10_1_2_2_3_0_2_0_0 9 56995 11   8,[2]            
Line: 879 to 879
 
  10_1_2_3_2_0_0_0_2 10 352 13   9,[2]            
  10_1_2_3_2_0_1_0_0_0_1 10 50 15   9,[2]   a 10      
  10_1_2_3_2_0_2_0_0 9 27665 11   8,[2]            
Changed:
<
<
  10_1_2_3_3_0_0_0_1 9 3363 13   8,[2]            
>
>
  10_1_2_3_3_0_0_0_1 9 3363 13   8,[2]   a' 10, #248,β      
 
  10_1_2_3_4_0_0_0_0 8 29773 10   7,[2]            
Changed:
<
<
  10_1_2_4_0_0_2_0_1 10 1056 13   9,[2]            
>
>
  10_1_2_4_0_0_2_0_1 10 1056 13   9,[2]   a' 10, #455, β      
 
  10_1_2_4_1_0_0_0_2 10 467 13   9,[2]            
  10_1_2_4_1_0_1_0_0_0_1 10 22 15   9,[2]   a 10      
  10_1_2_4_1_0_2_0_0 9 5678 12   8,[2]            
Line: 912 to 912
 
  10_1_3_1_0_0_5_0_0 10 237 13   9,[2]            
  10_1_3_1_1_0_1_0_3 11 16 15   10,[2]            
  10_1_3_1_1_0_3_0_1 10 1402 13   9,[2]            
Changed:
<
<
  10_1_3_1_2_0_1_0_2 10 900 13   9,[2]            
>
>
  10_1_3_1_2_0_1_0_2 10 900 13   9,[2]   a' 10, #534,β      
 
  10_1_3_1_2_0_2_0_0_0_1 10 26 15   9,[2]   a 10      
  10_1_3_1_2_0_3_0_0 9 27157 12   8,[2]            
  10_1_3_1_3_0_0_0_1_0_1 10 1 15   9,[2]   a 10 *    
Line: 1001 to 1001
 
  10_1_5_3_0_0_1_0_0 7 13489 11   6,[2]            
  10_1_6_0_0_0_0_0_3 9 7 15   8,[2]            
  10_1_6_0_0_0_1_0_1_0_1 9 6 15   8,[2]   a 10      
Changed:
<
<
  10_1_6_0_0_0_2_0_1 8 2343 13   7,[2]            
>
>
  10_1_6_0_0_0_2_0_1 8 2343 13   7,[2]   a' 10, #1,β      
 
  10_1_6_0_1_0_0_0_2 8 242 14   7,[2]            
  10_1_6_0_1_0_1_0_0_0_1 8 8 15   7,[2]   a 10      
  10_1_6_0_1_0_2_0_0 7 34729 11   6,[2]            
Line: 1031 to 1031
 
  10_2_0_0_6_0_0_0_2 10 14 14   9,[2]            
  10_2_0_0_6_0_1_0_0_0_1 10 2 15   9,[2]   a 10      
  10_2_0_0_6_0_2_0_0 9 1070 12   8,[2]            
Changed:
<
<
  10_2_0_0_7_0_0_0_1 9 77 13   8,[2]            
>
>
  10_2_0_0_7_0_0_0_1 9 77 13   8,[2]   a' 10, #53,β      
 
  10_2_0_0_8_0_0_0_0 8 465 10   7,[2]            
  10_2_0_1_2_0_4_0_1 11 28 14   10,[2]            
  10_2_0_1_3_0_2_0_2 11 59 14   10,[2]            
Line: 1041 to 1041
 
  10_2_0_1_5_0_0_0_2 10 53 14   9,[2]            
  10_2_0_1_5_0_1_0_0_0_1 10 7 15   9,[2]   a 10      
  10_2_0_1_5_0_2_0_0 9 3786 12   8,[2]            
Changed:
<
<
  10_2_0_1_6_0_0_0_1 9 382 13   8,[2]            
>
>
  10_2_0_1_6_0_0_0_1 9 382 13   8,[2]   a' 10, #242,β      
 
  10_2_0_1_7_0_0_0_0 8 1288 12   7,[2]            
  10_2_0_2_0_0_4_0_2 12 8 14   11,[2]   b 10, #7      
  10_2_0_2_0_0_6_0_0 11 5 14   10,[2]            
Line: 1052 to 1052
 
  10_2_0_2_2_0_4_0_0 10 793 12   9,[2]            
  10_2_0_2_3_0_0_0_3 11 1 15   10,[2]       *    
  10_2_0_2_3_0_1_0_1_0_1 11 1 15   10,[2]   a 10 *    
Changed:
<
<
  10_2_0_2_3_0_2_0_1 10 1103 13   9,[2]            
>
>
  10_2_0_2_3_0_2_0_1 10 1103 13   9,[2]   a' 10, #2,β      
 
  10_2_0_2_4_0_0_0_2 10 359 12   9,[2]   a,c 10, #1      
  10_2_0_2_4_0_1_0_0_0_1 10 3 15   9,[2]   a 10      
  10_2_0_2_4_0_2_0_0 9 8297 10   8,[2]   c        
Line: 1138 to 1138
 
  10_2_1_4_1_0_1_0_1 9 648 12   8,[2]   a 10, #1      
  10_2_1_4_2_0_0_0_0_0_1 9 1 15   8,[2]   a 10 *    
  10_2_1_4_2_0_1_0_0 8 20783 10   7,[2]            
Changed:
<
<
  10_2_1_5_0_0_1_0_1 9 120 13   8,[2]            
>
>
  10_2_1_5_0_0_1_0_1 9 120 13   8,[2]   a' 10, #10,β      
 
  10_2_1_5_1_0_1_0_0 8 3791 12   7,[2]            
  10_2_1_6_0_0_1_0_0 8 5 15   7,[2]            
  10_2_2_0_0_0_6_0_0 10 13 14   9,[2]            
Line: 1252 to 1252
 
  10_2_5_0_1_0_0_0_1_0_1 8 1 15   7,[2]   a 10 *    
  10_2_5_0_1_0_1_0_1 7 12947 12   6,[2]   a 10, #83      
  10_2_5_0_2_0_0_0_0_0_1 7 8 15   6,[2]   a 10      
Changed:
<
<
  10_2_5_0_2_0_1_0_0 6 330437 10   5,[2]            
>
>
  10_2_5_0_2_0_1_0_0 6 330437 10   5,[2]   a' 10, #27,β      
 
  10_2_5_1_0_0_1_0_1 7 5048 12   6,[2]   a 10, #31      
  10_2_5_1_1_0_0_0_0_0_1 7 12 15   6,[2]   a 10      
  10_2_5_1_1_0_1_0_0 6 178262 10   5,[2]            
Line: 1371 to 1371
 
  10_3_3_0_1_0_3_0_0 7 15004 11   6,[2]            
  10_3_3_0_2_0_1_0_1 7 16159 12   6,[2]   a 10, #43      
  10_3_3_0_3_0_0_0_0_0_1 7 8 15   6,[2]   a 10      
Changed:
<
<
  10_3_3_0_3_0_1_0_0 6 333695 10   5,[2]            
>
>
  10_3_3_0_3_0_1_0_0 6 333695 10   5,[2]   a' 10, #189,β      
 
  10_3_3_1_0_0_1_0_2 8 172 14   7,[2]            
  10_3_3_1_0_0_2_0_0_0_1 8 16 15   7,[2]   a 10      
  10_3_3_1_0_0_3_0_0 7 10786 11   6,[2]            
Line: 1619 to 1619
 
  10_8_0_2_0_0_0_0_0 2 182734 6   2,[] Z a 8,N2      
  10_8_1_0_0_0_1_0_0 2 83131 9   1,[2]   a        
  10_8_2_0_0_0_0_0_0 1 2259065 3   0,[2]   a 7      
Changed:
<
<
  10_9_0_0_0_0_0_0_1 2 265 12   1,[2]   a 10, #43 *    
>
>
  10_9_0_0_0_0_0_0_1 2 265 12   1,[2]   a 10, #43      
 
  10_9_0_0_1_0_0_0_0 1 105737 6   0,[2]   a 9, #1      
  10_9_0_1_0_0_0_0_0 1 133745 6   Z Z a 8,N4      
  10_10_0_0_0_0_0_0_0_a 0 177 10 Z Z Z     *    

Revision 492017-08-03 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 1619 to 1619
 
  10_8_0_2_0_0_0_0_0 2 182734 6   2,[] Z a 8,N2      
  10_8_1_0_0_0_1_0_0 2 83131 9   1,[2]   a        
  10_8_2_0_0_0_0_0_0 1 2259065 3   0,[2]   a 7      
Changed:
<
<
  10_9_0_0_0_0_0_0_1 2 265 12   1,[2]   a 10, #43      
>
>
  10_9_0_0_0_0_0_0_1 2 265 12   1,[2]   a 10, #43 *    
 
  10_9_0_0_1_0_0_0_0 1 105737 6   0,[2]   a 9, #1      
  10_9_0_1_0_0_0_0_0 1 133745 6   Z Z a 8,N4      
  10_10_0_0_0_0_0_0_0_a 0 177 10 Z Z Z     *    

Revision 482017-05-11 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 1329 to 1329
 
  10_3_1_3_0_0_1_0_2 9 4 15   8,[2]            
  10_3_1_3_0_0_3_0_0 8 895 12   7,[2]   b 10, #81      
  10_3_1_3_1_0_1_0_1 8 1017 13   7,[2]            
Changed:
<
<
  10_3_1_3_2_0_0_0_0_0_1 8 4 15   7,[2]   a,b 10      
>
>
  10_3_1_3_2_0_0_0_0_0_1 8 4 15   7,[2]   a 10      
 
  10_3_1_3_2_0_1_0_0 7 43011 10   6,[2]   b        
  10_3_1_4_0_0_1_0_1 8 145 13   7,[2]            
  10_3_1_4_1_0_1_0_0 7 3237 12   6,[2]            

Revision 472017-05-10 - EdwardSwartz

Line: 1 to 1
 
META TOPICPARENT name="WebHome"
-- Main.ebs22 - 2016-01-07 -- Main.srs74 - 2015-12-22
Line: 26 to 26
 
  • b - If n is the number of singular vertices, then g2 ≥ 2 χ - ( n-3 choose 3). If n-3 < 3, then the binomial coefficient is interepreted as zero.
  • c - If Δ has 8 singular vertices and m of them are Klein bottles, then g2 ≥ 2 χ - 10 + (m/3)
  • d - If Δ has 8 singular vertices and any of them are real projective planes, then g2 ≥ 2 χ - 7
Added:
>
>
  • e - If Δ has 8 singular vertices including 3 projective planes and 2 Klein bottles, then g2 ≥ 2 χ - 5
 

f-vector - A nonempty entry indicates that all possible f-vectors for complexes with the given singular vertices is known.

Line: 1196 to 1197
 
  10_2_3_0_1_0_3_0_1 9 1161 13   8,[2]            
  10_2_3_0_2_0_1_0_2 9 476 14   8,[2]            
  10_2_3_0_2_0_2_0_0_0_1 9 22 15   8,[2]   a 10      
Changed:
<
<
  10_2_3_0_2_0_3_0_0 8 22217 11   7,[2]            
>
>
  10_2_3_0_2_0_3_0_0 8 22217 11   7,[2]   e 10, #2      
 
  10_2_3_0_3_0_0_0_1_0_1 9 6 15   8,[2]   a 10      
  10_2_3_0_3_0_1_0_1 8 13619 12   7,[2]   a 10, #127      
  10_2_3_0_4_0_0_0_0_0_1 8 10 15   7,[2]   a 10      

Revision 462017-05-02 - EdwardSwartz

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  10_1_1_5_1_0_1_0_1 10 1802 12   9,[2]   a 10, #33      
  10_1_1_5_2_0_0_0_0_0_1 10 2 15   9,[2]   a 10      
  10_1_1_5_2_0_1_0_0 9 13397 11   8,[2]            
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  10_1_1_6_0_0_1_0_1 10 72 13   9,[2]            
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  10_1_1_6_0_0_1_0_1 10 72 13   9,[2]   a' 10,#2,β      
 
  10_1_1_6_1_0_1_0_0 9 14302 9   8,[2]   a 10      
  10_1_1_7_0_0_1_0_0 9 41 12   8,[2]            
  10_1_2_0_0_0_6_0_1 12 2 15   11,[2]            

Revision 452017-05-01 - EdwardSwartz

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H1, H2, H3 - Integer homology groups of all of the triangulations with the given vertex links on 10 vertices. The homology group is trivial if blank. For H2 the shorthand n,[2] stands for the direct sum of Z/2Z and the free abelian group of rank n.

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Γ - A letter in this column indicates that the value of minG2 is the minimum of g2 over all triangulations of a three-dimensional normal pseudomanifold with the given singular vertices. See b' for an exception. The letter indicates the proof as follows:

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Γ - Γ is the minimum of g2 over all triangulations of a three-dimensional normal pseudomanifold with the given singular vertices. A letter in this column indicates that minG2=Γ and the proof is indicated below. A superscript ' indicates that Γ=minG2-1 and 11 vertices are needed to realize Γ.

 
  • a - For any vertex v of Δ, g2(Δ) ≥ g2 (link v).
  • b - If n is the number of singular vertices, then g2 ≥ 2 χ - ( n-3 choose 3). If n-3 < 3, then the binomial coefficient is interepreted as zero.
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  • b' - Same theorem, with the minimum g2 realized by a complex with 11 vertices. Hence Γ = minG2 - 1.
 
  • c - If Δ has 8 singular vertices and m of them are Klein bottles, then g2 ≥ 2 χ - 10 + (m/3)
  • d - If Δ has 8 singular vertices and any of them are real projective planes, then g2 ≥ 2 χ - 7
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  • d' - Same theorem, with the minimum g2 realized by a complex with 11 vertices. Hence Γ = minG2 - 1.
 

f-vector - A nonempty entry indicates that all possible f-vectors for complexes with the given singular vertices is known.

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  10_2_0_5_1_0_2_0_0 9 11781 9   8,[2]   a        
  10_2_0_5_2_0_0_0_1 9 400 12   8,[2]   a 10, #5      
  10_2_0_5_3_0_0_0_0 8 1507 12   7,[2]            
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  10_2_0_6_0_0_0_0_2 10 6 13   9,[2]            
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  10_2_0_6_0_0_0_0_2 10 6 13   9,[2]   a' 10,#5,β *    
 
  10_2_0_6_0_0_2_0_0 9 2861 9   8,[2]   a        
  10_2_0_6_1_0_0_0_1 9 13 14   8,[2]            
  10_2_0_8_0_0_0_0_0 8 10883 6   8,[] Z a,b 8,N1      

Revision 442017-04-28 - EdwardSwartz

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  • b' - Same theorem, with the minimum g2 realized by a complex with 11 vertices. Hence Γ = minG2 - 1.
  • c - If Δ has 8 singular vertices and m of them are Klein bottles, then g2 ≥ 2 χ - 10 + (m/3)
  • d - If Δ has 8 singular vertices and any of them are real projective planes, then g2 ≥ 2 χ - 7
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  • d' - Same theorem, with the minimum g2 realized by a complex with 11 vertices. Hence Γ = minG2 - 1.
 

f-vector - A nonempty entry indicates that all possible f-vectors for complexes with the given singular vertices is known.

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  10_2_1_0_6_0_1_0_0 8 8682 11   7,[2]            
  10_2_1_1_1_0_3_0_2 11 6 15   10,[2]   d 10      
  10_2_1_1_1_0_4_0_0_0_1 11 1 15   10,[2]   a,d 10 *    
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  10_2_1_1_1_0_5_0_0 10 92 14   9,[2]            
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  10_2_1_1_1_0_5_0_0 10 92 14   9,[2]   d' 10,#3,β      
 
  10_2_1_1_2_0_1_0_3 11 2 15   10,[2]   d 10      
  10_2_1_1_2_0_3_0_1 10 421 14   9,[2]            
  10_2_1_1_3_0_1_0_2 10 232 14   9,[2]            

Revision 432017-04-26 - EdwardSwartz</