生成非星形子空间的微相交子空间的安扎尔定理 I：交映和赫米提形式

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-07-09 DOI:10.1016/j.laa.2024.07.004

Maarten De Boeck , Geertrui Van de Voorde

{"title":"生成非星形子空间的微相交子空间的安扎尔定理 I：交映和赫米提形式","authors":"Maarten De Boeck , Geertrui Van de Voorde","doi":"10.1016/j.laa.2024.07.004","DOIUrl":null,"url":null,"abstract":"<div>In this paper, we solve a classical counting problem for non-degenerate forms of symplectic and hermitian type defined on a vector space: given a subspace π, we find the number of non-singular subspaces that are trivially intersecting with π and span a non-singular subspace with π. Lower bounds for the quantity of such pairs where π is non-singular were first studied in “Glasby, Niemeyer, Praeger (Finite Fields Appl., 2022)”, which was later improved in “Glasby, Ihringer, Mattheus (Des. Codes Cryptogr., 2023)” and generalised in “Glasby, Niemeyer, Praeger (Linear Algebra Appl., 2022)”. In this paper, we derive explicit formulae, which allow us to give the exact proportion and improve the known lower bounds.</div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Anzahl theorems for trivially intersecting subspaces generating a non-singular subspace I: Symplectic and hermitian forms\",\"authors\":\"Maarten De Boeck , Geertrui Van de Voorde\",\"doi\":\"10.1016/j.laa.2024.07.004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>In this paper, we solve a classical counting problem for non-degenerate forms of symplectic and hermitian type defined on a vector space: given a subspace π, we find the number of non-singular subspaces that are trivially intersecting with π and span a non-singular subspace with π. Lower bounds for the quantity of such pairs where π is non-singular were first studied in “Glasby, Niemeyer, Praeger (Finite Fields Appl., 2022)”, which was later improved in “Glasby, Ihringer, Mattheus (Des. Codes Cryptogr., 2023)” and generalised in “Glasby, Niemeyer, Praeger (Linear Algebra Appl., 2022)”. In this paper, we derive explicit formulae, which allow us to give the exact proportion and improve the known lower bounds.</div>\",\"PeriodicalId\":18043,\"journal\":{\"name\":\"Linear Algebra and its Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Linear Algebra and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0024379524002866\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0024379524002866","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们解决了定义在矢量空间上的交映型和赫米特型非退化形式的经典计数问题：给定子空间π，我们求出与π三交且与π跨非矢量子空间的非矢量子空间的数量。π为非矢量时，此类对的数量下限在 "Glasby, Niemeyer, Praeger (Finite Fields Appl、2022）"中首次研究，后来在 "Glasby, Ihringer, Mattheus (Des. Codes Cryptogr., 2023) "中得到改进，并在 "Glasby, Niemeyer, Praeger (Linear Algebra Appl., 2022) "中得到推广。在本文中，我们推导出了明确的公式，从而可以给出精确的比例并改进已知的下限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Anzahl theorems for trivially intersecting subspaces generating a non-singular subspace I: Symplectic and hermitian forms

In this paper, we solve a classical counting problem for non-degenerate forms of symplectic and hermitian type defined on a vector space: given a subspace π, we find the number of non-singular subspaces that are trivially intersecting with π and span a non-singular subspace with π. Lower bounds for the quantity of such pairs where π is non-singular were first studied in “Glasby, Niemeyer, Praeger (Finite Fields Appl., 2022)”, which was later improved in “Glasby, Ihringer, Mattheus (Des. Codes Cryptogr., 2023)” and generalised in “Glasby, Niemeyer, Praeger (Linear Algebra Appl., 2022)”. In this paper, we derive explicit formulae, which allow us to give the exact proportion and improve the known lower bounds.

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

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.