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found a counterexample

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This commit is contained in:
Yu Cong
2025-10-24 16:02:48 +08:00
parent 18b69540bc
commit 1363de0328
2 changed files with 10 additions and 0 deletions
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9
projection.out
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@@ -6,3 +6,12 @@ n=7 , m=10 graph gap = 1 projection gap = 2 factor=2
[1 0 0 1 0 0 1 0 0 0 1]
[0 1 0 0 1 0 0 1 0 0 1]
[0 0 1 0 0 1 0 0 1 1 1]
n=8 , m=14 graph gap = 1 projection gap = 15/7 factor=15/7 max=2.1428571428571432
[1 1 1 0 0 0 0 0 0 0 0 0 0 0 1]
[0 0 0 1 1 1 0 0 0 0 0 0 0 0 1]
[0 0 0 0 0 0 1 1 1 0 0 0 0 0 1]
[0 0 0 0 0 0 0 0 0 1 1 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1]
[1 0 0 1 0 0 1 0 0 1 0 0 0 0 1]
[0 1 0 0 1 0 0 1 0 0 1 0 1 0 1]
[0 0 1 0 0 1 0 0 1 0 0 1 0 1 1]

1
projection.sage
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@@ -1,5 +1,6 @@
# cogirth-packing gap of projections of graphic matroids
# see if gap(projection) <= 2 * gap(graph)
# this is wrong. see the last matrix in projection.out
from sage.all import *
from sage.matroids.all import *