On the toric ideal of a matroid

Michal Lason*, Mateusz Michalek

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Describing minimal generating set of a toric ideal is a well-studied and difficult problem. In 1980 White conjectured that the toric ideal associated to a matroid is equal to the ideal generated by quadratic binomials corresponding to symmetric exchanges.

We prove White's conjecture up to saturation, that is that the saturations of both ideals are equal. In the language of algebraic geometry this means that both ideals define the same projective scheme. Additionally we prove the full conjecture for strongly base orderable niatroids. (C) 2014 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalADVANCES IN MATHEMATICS
Volume259
DOIs
Publication statusPublished - 10 Jul 2014
MoE publication typeA1 Journal article-refereed

Keywords

  • Matroid
  • Toric ideal
  • Base exchange
  • Strongly base orderable matroid
  • POLYMATROIDS

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