Alternatives for the q-matroid axioms of independent spaces, bases, and spanning spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-25 DOI:10.1016/j.aam.2023.102632

Michela Ceria , Relinde Jurrius

引用次数: 0

Abstract

It is well known that in q-matroids, axioms for independent spaces, bases, and spanning spaces differ from the classical case of matroids, since the straightforward q-analogue of the classical axioms does not give a q-matroid. For this reason, a fourth axiom has been proposed. In this paper we show how we can describe these spaces with only three axioms, providing two alternative ways to do that. As an application, we show direct cryptomorphisms between independent spaces and circuits and between independent spaces and bases.

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独立空间、基和生成空间的q-矩阵公理的替代方法

众所周知，在q-拟阵中，独立空间、基和生成空间的公理不同于经典的拟阵，因为经典公理的直接q-类比并没有给出一个q-拟阵。出于这个原因，我们提出了第四个公理。在本文中，我们展示了如何只用三个公理来描述这些空间，并提供了两种替代方法来做到这一点。作为一个应用，我们证明了独立空间与电路之间以及独立空间与基之间的直接隐型。

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

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.