From 1c9e29016e54fca10e81b10b207e5c0fd75717ea Mon Sep 17 00:00:00 2001
From: Yu Cong <sxlxcsxlxc@gmail.com>
Date: Tue, 16 Dec 2025 13:55:23 +0800
Subject: [PATCH] z

---
 main.tex | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/main.tex b/main.tex
index 3531c28..11e9027 100644
--- a/main.tex
+++ b/main.tex
@@ -169,8 +169,8 @@ Then we have
 
 For general matroids, we want to show the following.
 
-\begin{conjecture}
-Let $M'$ be the contraction $M/F^*$. The rank of $M'$ is $k$. 
+\begin{conjecture}\label{conj:dist}
+Let $M'$ be the contraction minor $M/F^*$. The rank of $M'$ is $k$. 
 Given a positive integer $k'<k$, then there exists a distribution on $k'$-cocycles such that
 for any base $B$ of $M'$, the expected size of intersection is at most $O(k')$.
 \end{conjecture}
@@ -212,6 +212,10 @@ For a subset of rigid components $\mathcal P$, let $t=|\bigcup_{P\in \mathcal P}
 One can see that in this process we do not care the actual base $B_{F^*}$ and only the 1-thin cover matters.
 \end{remark}
 
+\begin{conjecture}
+\autoref{conj:dist} is true when $M$ is a 2D rigidity matroid.
+\end{conjecture}
+
 \section{Greedy base packing}