English

On the toric ideals of matroids of a fixed rank

Combinatorics 2021-12-01 v5 Commutative Algebra Algebraic Geometry

Abstract

In 19801980 White conjectured that every element of the toric ideal of a matroid is generated by quadratic binomials corresponding to symmetric exchanges. We prove White's conjecture for high degrees with respect to the rank. This extends our result arXiv:1302.5236 confirming White's conjecture `up to saturation'. Furthermore, we study degrees of Gr\"{o}bner bases and Betti tables of the toric ideals of matroids of a fixed rank.

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Cite

@article{arxiv.1601.08199,
  title  = {On the toric ideals of matroids of a fixed rank},
  author = {Michał Lasoń},
  journal= {arXiv preprint arXiv:1601.08199},
  year   = {2021}
}

Comments

final version, 16 pages