English

Gr\"obner bases of toric ideals associated with matroids

Commutative Algebra 2020-04-28 v2 Combinatorics

Abstract

In 1980, White conjectured that the toric ideal of a matroid is generated by quadratic binomials corresponding to a symmetric exchange. In this paper, we compute Gr\"obner bases of toric ideals associated with matroids and show that, for every matroid on ground sets of size at most seven except for two matroids, Gr\"obner bases of toric ideals consist of quadratic binomials corresponding to a symmetric exchange.

Keywords

Cite

@article{arxiv.2001.11835,
  title  = {Gr\"obner bases of toric ideals associated with matroids},
  author = {Ken-ichi Hayase and Takayuki Hibi and Koyo Katsuno and Kazuki Shibata},
  journal= {arXiv preprint arXiv:2001.11835},
  year   = {2020}
}

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4 pages