{"title":"Alternatives for the q-matroid axioms of independent spaces, bases, and spanning spaces","authors":"Michela Ceria , Relinde Jurrius","doi":"10.1016/j.aam.2023.102632","DOIUrl":null,"url":null,"abstract":"<div><p>It is well known that in <em>q</em>-matroids, axioms for independent spaces, bases, and spanning spaces differ from the classical case of matroids, since the straightforward <em>q</em>-analogue of the classical axioms does not give a <em>q</em>-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.</p></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"153 ","pages":"Article 102632"},"PeriodicalIF":1.3000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0196885823001501","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/10/25 0:00:00","PubModel":"Epub","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
