论与帕斯卡三角形有关的矩阵行列式

IF 0.6 3区数学 Q3 MATHEMATICS

Periodica Mathematica Hungarica Pub Date : 2024-06-18 DOI:10.1007/s10998-024-00581-6

Martín Mereb

{"title":"论与帕斯卡三角形有关的矩阵行列式","authors":"Martín Mereb","doi":"10.1007/s10998-024-00581-6","DOIUrl":null,"url":null,"abstract":"We prove that the symmetric Pascal triangle matrix modulo 2 has the property that each of the square sub-matrices positioned at the upper border or on the left border has determinant, computed in \\({\\mathbb {Z}}\\), equal to 1 or \\(-1\\). Furthermore, we give the exact number of Pascal-like \\(n \\times m\\) matrices over a commutative ring with finite group of units.\n","PeriodicalId":49706,"journal":{"name":"Periodica Mathematica Hungarica","volume":"31 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On determinants of matrices related to Pascal’s triangle\",\"authors\":\"Martín Mereb\",\"doi\":\"10.1007/s10998-024-00581-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the symmetric Pascal triangle matrix modulo 2 has the property that each of the square sub-matrices positioned at the upper border or on the left border has determinant, computed in \\\\({\\\\mathbb {Z}}\\\\), equal to 1 or \\\\(-1\\\\). Furthermore, we give the exact number of Pascal-like \\\\(n \\\\times m\\\\) matrices over a commutative ring with finite group of units.\\n\",\"PeriodicalId\":49706,\"journal\":{\"name\":\"Periodica Mathematica Hungarica\",\"volume\":\"31 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-06-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Periodica Mathematica Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10998-024-00581-6\",\"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":"Periodica Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10998-024-00581-6","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

我们证明了对称帕斯卡三角形矩阵 modulo 2 具有这样的性质，即位于上边界或左边界的每个正方形子矩阵的行列式，在 \({\mathbb {Z}}\) 中计算，都等于 1 或 \(-1\)。此外，我们还给出了在具有有限单元组的交换环上帕斯卡样（n 次 m\ ）矩阵的确切数目。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On determinants of matrices related to Pascal’s triangle

查看原文本刊更多论文

On determinants of matrices related to Pascal’s triangle

We prove that the symmetric Pascal triangle matrix modulo 2 has the property that each of the square sub-matrices positioned at the upper border or on the left border has determinant, computed in \({\mathbb {Z}}\), equal to 1 or \(-1\). Furthermore, we give the exact number of Pascal-like \(n \times m\) matrices over a commutative ring with finite group of units.

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

Periodica Mathematica Hungarica 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Periodica Mathematica Hungarica is devoted to publishing research articles in all areas of pure and applied mathematics as well as theoretical computer science. To be published in the Periodica, a paper must be correct, new, and significant. Very strong submissions (upon the consent of the author) will be redirected to Acta Mathematica Hungarica. Periodica Mathematica Hungarica is the journal of the Hungarian Mathematical Society (János Bolyai Mathematical Society). The main profile of the journal is in pure mathematics, being open to applied mathematical papers with significant mathematical content.