Maximal Matroids in Weak Order Posets

Bill Jackson; Shin-ichi Tanigawa

Maximal Matroids in Weak Order Posets

Combinatorics 2021-03-16 v2

Authors: Bill Jackson , Shin-ichi Tanigawa

Abstract

Let $\cX$ be a family of subsets of a finite set $E$ . A matroid on $E$ is called an $\cX$ -matroid if each set in $\cX$ is a circuit. We consider the problem of determining when there exists a unique maximal $\cX$ -matroid in the weak order poset of all $\cX$ -matroids on $E$ , and characterizing its rank function when it exists.

Keywords

matroid theory partially ordered sets

Cite

@article{arxiv.2102.09901,
  title  = {Maximal Matroids in Weak Order Posets},
  author = {Bill Jackson and Shin-ichi Tanigawa},
  journal= {arXiv preprint arXiv:2102.09901},
  year   = {2021}
}

Comments

typographical corrections, exposition improvements

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