From 2e3acd6cd6e6e0f257d9698adccc06fa7e41a442 Mon Sep 17 00:00:00 2001 From: Yu Cong Date: Wed, 3 Dec 2025 11:28:04 +0800 Subject: [PATCH] z --- main.tex | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/main.tex b/main.tex index 4d633ad..085f879 100644 --- a/main.tex +++ b/main.tex @@ -149,8 +149,10 @@ However, Lemma~7 in \cite{Thorup_2008} does not generalize to all matroids and w \subsection{Support size} -Recall that we construct the ideal tree packing recursively. Suppose that the ideal base packing for $M|F^*$ is has $n$ bases and let $m$ be the size of support of the optimal base packing of $M$. Then the number of bases in the ideal base packing of $M$ is $nm$. Note that $m$ is upperbounded by the size of the groundset. -So the support size can be exponential. +Recall that we construct the ideal base packing recursively. Suppose that the ideal base packing for $M|F^*$ is has $n$ bases and let $m$ be the size of support of the optimal base packing of $M$. Then the number of bases in the ideal base packing of $M$ is $nm$. Note that $m$ is upperbounded by the size of the groundset. +The support size can be exponential. Consider a path with $n$ points and parallel edges. The depth of recursion can be $n-1$. + +Do we need all bases in the packing? \subsection{Rigidity matroids} \begin{conjecture}\label{conj:idealrigidbase}