Tutte多项式Merino-Welsh猜想的无关结果

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-02-19 DOI:10.1016/j.aam.2025.102866

Joseph P.S. Kung

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引用次数: 0

摘要

我们给出了一个秩-r无循环矩阵M上成立加性Merino-Welsh不等式的两个充分条件。第一个是M的密度足够大。第二是M的所有共电路至少有r+1个元素。从某种意义上说，这些结果是“无关紧要的”，尽管它们表明了这个猜想的一个版本适用于许多拟阵，但它们远远不能涵盖所有可能的情况。

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Inconsequential results on the Merino-Welsh conjecture for Tutte polynomials

We present two sufficient conditions on a rank-r coloop-free matroid M for the additive Merino-Welsh inequality to hold. The first is that the density of M is sufficiently large. The second is that all the cocircuits of M have at least

r + 1

elements. These results are “inconsequential” in the sense that although they show that a version of the conjecture holds for many matroids, they are far from covering all the possible cases.

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.