From 1363de03281c2e8e4284d19c21747e2eb8b92d99 Mon Sep 17 00:00:00 2001
From: Yu Cong <sxlxcsxlxc@gmail.com>
Date: Fri, 24 Oct 2025 16:02:48 +0800
Subject: [PATCH] found a counterexample

---
 projection.out  | 9 +++++++++
 projection.sage | 1 +
 2 files changed, 10 insertions(+)

diff --git a/projection.out b/projection.out
index 6afb851..84494b2 100644
--- a/projection.out
+++ b/projection.out
@@ -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]
diff --git a/projection.sage b/projection.sage
index e12b9c1..eedf659 100644
--- a/projection.sage
+++ b/projection.sage
@@ -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 *