Graphs of relations and Hilbert series

被引：8

作者：

Cameron, Peter ^{[1
]}

Iyudu, Natalia ^{[1
]}

机构：

[1] Queen Mary Univ London, London, England

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2007年 / 42卷 / 11-12期

关键词：

quadratic algebra; Hilbert series; Grobner basis; colored graph;

D O I：

10.1016/j.jsc.2007.07.006

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by n generators and n(n-1)/2 relations for n <= 7. Then we investigate combinatorial structure of colored graph associated with relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated with each color are pairwise 2-isomorphic. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：1066 / 1078

页数：13

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