sxlxc/ideal-base-packing
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases 1 Wiki Activity

z
All checks were successful
build pdf / build (push) Successful in 4s
Details

Browse Source
This commit is contained in:
Yu Cong
2025-12-16 13:55:23 +08:00
parent 917c41843c
commit 1c9e29016e
1 changed files with 6 additions and 2 deletions
Download Patch File Download Diff File Expand all files Collapse all files

8
main.tex
View File

@@ -169,8 +169,8 @@ Then we have
For general matroids, we want to show the following. For general matroids, we want to show the following.
\begin{conjecture} \begin{conjecture}\label{conj:dist}
Let $M'$ be the contraction $M/F^*$. The rank of $M'$ is $k$. 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 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 $O(k')$. for any base $B$ of $M'$, the expected size of intersection is at most $O(k')$.
\end{conjecture} \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. 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} \end{remark}
\begin{conjecture}
\autoref{conj:dist} is true when $M$ is a 2D rigidity matroid.
\end{conjecture}
\section{Greedy base packing} \section{Greedy base packing}