q-matroid 的循环平面

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Algebraic Combinatorics Pub Date : 2024-05-09 DOI:10.1007/s10801-024-01321-2

Gianira N. Alfarano, Eimear Byrne

{"title":"q-matroid 的循环平面","authors":"Gianira N. Alfarano, Eimear Byrne","doi":"10.1007/s10801-024-01321-2","DOIUrl":null,"url":null,"abstract":"In this paper we develop the theory of cyclic flats of q-matroids. We show that the cyclic flats, together with their ranks, uniquely determine a q-matroid and hence derive a new q-cryptomorphism. We introduce the notion of \\(\\mathbb {F}_{q^m}\\)-independence of an \\(\\mathbb {F}_q\\)-subspace of \\(\\mathbb {F}_q^n\\) and we show that q-matroids generalize this concept, in the same way that matroids generalize the notion of linear independence of vectors over a given field.\n","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":"139 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The cyclic flats of a q-matroid\",\"authors\":\"Gianira N. Alfarano, Eimear Byrne\",\"doi\":\"10.1007/s10801-024-01321-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we develop the theory of cyclic flats of q-matroids. We show that the cyclic flats, together with their ranks, uniquely determine a q-matroid and hence derive a new q-cryptomorphism. We introduce the notion of \\\\(\\\\mathbb {F}_{q^m}\\\\)-independence of an \\\\(\\\\mathbb {F}_q\\\\)-subspace of \\\\(\\\\mathbb {F}_q^n\\\\) and we show that q-matroids generalize this concept, in the same way that matroids generalize the notion of linear independence of vectors over a given field.\\n\",\"PeriodicalId\":14926,\"journal\":{\"name\":\"Journal of Algebraic Combinatorics\",\"volume\":\"139 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10801-024-01321-2\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10801-024-01321-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们发展了 q-matroids的循环平面理论。我们证明了循环平面连同它们的等级唯一地决定了一个 q-matroid，并由此推导出一个新的 q-密码同构。我们引入了 \(\mathbb {F}_{q^m}\)-independence of an \(\mathbb {F}_q\)-subspace of \(\mathbb {F}_q^n\)子空间的 \(\mathbb {F}_{q^m}\)-independence 概念，并证明了 q-matroids 对这个概念的概括，就像 matroids 对给定域上向量的线性独立性概念的概括一样。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The cyclic flats of a q-matroid

查看原文本刊更多论文

The cyclic flats of a q-matroid

In this paper we develop the theory of cyclic flats of q-matroids. We show that the cyclic flats, together with their ranks, uniquely determine a q-matroid and hence derive a new q-cryptomorphism. We introduce the notion of \(\mathbb {F}_{q^m}\)-independence of an \(\mathbb {F}_q\)-subspace of \(\mathbb {F}_q^n\) and we show that q-matroids generalize this concept, in the same way that matroids generalize the notion of linear independence of vectors over a given field.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Algebraic Combinatorics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.