Tutte多项式解释之间的一一对应关系

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

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

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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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