Tutte多项式解释之间的一一对应关系

IF 1.3 1区数学 Q1 MATHEMATICS Journal of Combinatorial Theory Series B Pub Date : 2023-09-01 Epub Date: 2023-05-26 DOI:10.1016/j.jctb.2023.05.002

Martin Kochol

引用次数: 1

摘要

我们研究了拟阵透视图M1的Tutte多项式的两种解释之间的关系→M2在以线性排序<；。一种众所周知的解释使用在M1中独立并在M2中跨越的集合的族B（M1，M2）上的内部和外部活动。最近，我们介绍了另一种基于M1的“环状碱基”家族D（M1，M2；<；）的解释→M2相对于<；。我们引入了B（M1，M2）和D（M1，M2<；）之间的一对一对应关系，它也产生了拟阵视角的Tutte多项式的解释之间的关系，并与对偶性相对应。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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One-to-one correspondence between interpretations of the Tutte polynomials

We study relation between two interpretations of the Tutte polynomial of a matroid perspective $M_{1} \to M_{2}$ on a set E given with a linear ordering <. A well known interpretation uses internal and external activities on a family $B (M_{1}, M_{2})$ of the sets independent in $M_{1}$ and spanning in $M_{2}$ . Recently we introduced another interpretation based on a family $D (M_{1}, M_{2}; <)$ of “cyclic bases” of $M_{1} \to M_{2}$ with respect to <. We introduce a one-to-one correspondence between $B (M_{1}, M_{2})$ and $D (M_{1}, M_{2}; <)$ that also generates a relation between the interpretations of the Tutte polynomial of a matroid perspective and corresponds with duality.

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来源期刊

Journal of Combinatorial Theory Series B 数学-数学

CiteScore

2.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.

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