A generalization of weight polynomials to matroids

被引：11
|
作者：
Johnsen, Trygve [1 ]
Roksvold, Jan [1 ]
Verdure, Hugues [1 ]
机构：
[1] UiT Arctic Univ Norway, Dept Math & Stat, N-9037 Tromso, Norway
来源：
DISCRETE MATHEMATICS | 2016年 / 339卷 / 02期
关键词：
Matroid; Weight enumerator; Linear code; Stanley-Reisner ideal; Higher weights; Tutte polynomial;
D O I：
10.1016/j.disc.2015.10.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Generalizing polynomials previously studied in the context of linear codes, we define weight polynomials and an enumerator for a matroid M. Our main result is that these polynomials are determined by Betti numbers associated with No-graded minimal free resolutions of the Stanley-Reisner ideals of M and so-called elongations of M. Generalizing Greene's theorem from coding theory, we show that the enumerator of a matroid is equivalent to its Tutte polynomial. (c) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码：632 / 645
页数：14
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