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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-09-01 DOI:10.1016/j.jctb.2023.05.002

Martin Kochol

引用次数: 1

Abstract

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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Tutte多项式解释之间的一一对应关系

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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