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Gröbner Bases of Toric Ideals Associated with Matroids
Ken-ichi Hayase
,
Takayuki Hibi
,
Koyo Katsuno
,
Kazuki Shibata
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 Gröbner 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, Gröbner bases of toric ideals consist of quadratic binomials corresponding to a symmetric exchange.