# Difference: Pseudomanifold10Vertex (57 vs. 58)

#### Revision 582017-08-28 - Main.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

`<-- /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]

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