Many toric ideals generated by quadratic binomials possess no quadratic Groebner bases
Many toric ideals generated by quadratic binomials possess no quadratic Groebner bases
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许多由二次二项式生成的复曲面理想不具有二次 Groebner 基
DOI：
10.1016/j.jalgebra.2013.09.039
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
H. Ohsugi and A. Shikama
中科院分区：
文献类型：
--
作者：
T. Hibi;K. Nishiyama;H. Ohsugi and A. Shikama
设G是有限连通简单图，IG是G的边环K [G]的环面理想.本文研究了有限图G的性质，即IG是由二次二项式生成的，且IG不具有二次Gröbner基.首先，我们给出了具有上述性质的有限图的一个非平凡无穷级数。其次，我们实现了由二次二项式生成的IG的组合特征，并通过计算机搜索，我们对具有上述性质的有限图G进行了分类，最多8个顶点。
Let G be a finite connected simple graph and I G the toric ideal of the edge ring K [G] of G. In the present paper, we study finite graphs G with the property that I G is generated by quadratic binomials and I G possesses no quadratic Gröbner basis. First, we give a nontrivial infinite series of finite graphs with the above property. Second, we implement a combinatorial characterization for I G to be generated by quadratic binomials and, by means of the computer search, we classify the finite graphs G with the above property, up to 8 vertices.