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

页码：632 / 645

页数：14

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