From 359004a4c2525c7eea92f5912f8d3e78d7c6f3df Mon Sep 17 00:00:00 2001 From: Yu Cong Date: Wed, 3 Dec 2025 17:27:08 +0800 Subject: [PATCH] z --- main.tex | 3 +++ 1 file changed, 3 insertions(+) diff --git a/main.tex b/main.tex index 0a0ed85..7c1ff86 100644 --- a/main.tex +++ b/main.tex @@ -146,6 +146,9 @@ Note that Thorup used a greedy way to construct the cocycle $C$. Elements in $C$ These facts implies that the minimum $k$-cocycle has a smaller value $\sum c(e)u^*(e)$ than $C$. However, Lemma~7 in \cite{Thorup_2008} does not generalize to all matroids and we need to take a close look at the construction of $C$. +Let $k'$ be $r(E)-r(F^*)$ and we want to find the minimum $k$-cocycle. +Basically we need to do random contraction on $M/ F^*$. Let $\mathcal X$ be the set $\set{X|X=B\setminus F^* \land r(X)=k'}$. That is, we consider all bases that hitten by the $k'$-cocycle exactly $k'$ times and for each of them we collect the intersection with the $k'$-cocycle. +... \subsection{Support size}