Groebner bases of toric ideals associated with matroids
Groebner bases of toric ideals associated with matroids
复制标题
与拟阵相关的环面理想的 Groebner 基
DOI：
10.1007/s40306-021-00468-5
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Kazuki Shibata
中科院分区：
文献类型：
--
作者：
Ken-ichi Hayase;Takayuki Hibi;Koyo Katsuno;Kazuki Shibata
1980年，白色阐明，环面理想的拟阵是由二次二项式对应的对称交换。本文计算了与拟阵相关联的环面理想的Gröbner基，并证明了，对于除两个拟阵之外的大小至多为7的基集上的每个拟阵，环面理想的Gröbner基由对应于对称交换的二次二项式组成。
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.