关于循环图的部分等距的幺一元

IF 0.8 4区数学 Q2 MATHEMATICS

Turkish Journal of Mathematics Pub Date : 2023-09-25 DOI:10.55730/1300-0098.3460

VITOR H. FERNANDES, TANIA PAULISTA

{"title":"关于循环图的部分等距的幺一元","authors":"VITOR H. FERNANDES, TANIA PAULISTA","doi":"10.55730/1300-0098.3460","DOIUrl":null,"url":null,"abstract":"In this paper we consider the monoid $DPC_n$ of all partial isometries of an $n$-cycle graph $C_n$. We show that $DPC_n$ is the submonoid of the monoid of all oriented partial permutations on an $n$-chain whose elements are precisely all restrictions of a dihedral group of order $2n$. Our main aim is to exhibit a presentation of $DPC_n$. We also describe Green's relations of $DPC_n$ and calculate its cardinality and rank.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"On the monoid of partial isometries of a cycle graph\",\"authors\":\"VITOR H. FERNANDES, TANIA PAULISTA\",\"doi\":\"10.55730/1300-0098.3460\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we consider the monoid $DPC_n$ of all partial isometries of an $n$-cycle graph $C_n$. We show that $DPC_n$ is the submonoid of the monoid of all oriented partial permutations on an $n$-chain whose elements are precisely all restrictions of a dihedral group of order $2n$. Our main aim is to exhibit a presentation of $DPC_n$. We also describe Green's relations of $DPC_n$ and calculate its cardinality and rank.\",\"PeriodicalId\":51206,\"journal\":{\"name\":\"Turkish Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-09-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Turkish Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.55730/1300-0098.3460\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Turkish Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55730/1300-0098.3460","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 4

摘要

本文研究了一个$n$-环图$C_n$的所有部分等距的一元$DPC_n$。我们证明了$DPC_n$是$n$链上的所有定向部分置换的monooid的子monooid，该链的元素恰好是$2n$阶二面体群的所有限制。我们的主要目的是展示$DPC_n$的表示。我们还描述了$DPC_n$的Green关系，并计算了它的基数和秩。

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

On the monoid of partial isometries of a cycle graph

In this paper we consider the monoid $DPC_n$ of all partial isometries of an $n$-cycle graph $C_n$. We show that $DPC_n$ is the submonoid of the monoid of all oriented partial permutations on an $n$-chain whose elements are precisely all restrictions of a dihedral group of order $2n$. Our main aim is to exhibit a presentation of $DPC_n$. We also describe Green's relations of $DPC_n$ and calculate its cardinality and rank.

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

Turkish Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

161

审稿时长

6-12 weeks

期刊介绍： The Turkish Journal of Mathematics is published electronically 6 times a year by the Scientific and Technological Research Council of Turkey (TÜBİTAK) and accepts English-language original research manuscripts in the field of mathematics. Contribution is open to researchers of all nationalities.