移位和阈值拟阵

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-08-26 DOI:10.1016/j.dam.2025.08.038

Ethan Partida

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引用次数: 0

摘要

我们用阈拟阵的定义基的结构来描述一类阈拟阵。我们还给出了一个非阈值的移位矩阵的例子，回答了Deza和Onn的问题。我们通过探索阈值拟阵的表征结果来得出结论：我们给出了大小为n的基集上阈值拟阵同构类数的一个公式。这个枚举表明几乎所有移位的拟阵都不是阈值。我们还提出了一个多项式时间算法来检查一个矩阵是否为阈值，并提供了Deza和Onn的一些主要结果的替代和简化证明。

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Shifted and threshold matroids

We characterize the class of threshold matroids by the structure of their defining bases. We also give an example of a shifted matroid which is not threshold, answering a question of Deza and Onn. We conclude by exploring consequences of our characterization of threshold matroids: We give a formula for the number of isomorphism classes of threshold matroids on a ground set of size

n

. This enumeration shows that almost all shifted matroids are not threshold. We also present a polynomial-time algorithm to check if a matroid is threshold and provide alternative and simplified proofs of some of the main results of Deza and Onn.

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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.