On the toric ideals of matroids of a fixed rank
Combinatorics
2021-12-01 v5 Commutative Algebra
Algebraic Geometry
Abstract
In 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.
Keywords
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