Gröbner Bases of Toric Ideals Associated with Matroids

IF 0.3 Q4 MATHEMATICS
Ken-ichi Hayase, Takayuki Hibi, Koyo Katsuno, Kazuki Shibata
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引用次数: 1

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.

与拟阵相关的托里理想的Gröbner基
1980年,White猜想拟阵的复曲面理想是由对应于对称交换的二次二元数产生的。在本文中,我们计算了与拟阵相关的复曲面理想的Gröbner基,并证明了对于除两个拟阵外大小至多为7的地集上的每一个拟阵,复曲面理想中的Gróbner基底由对应于对称交换的二次二元数组成。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
23
期刊介绍: Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.
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