保序和降序变换的折叠的组合结果

IF 0.7 Q2 MATHEMATICS
E. Korkmaz
{"title":"保序和降序变换的折叠的组合结果","authors":"E. Korkmaz","doi":"10.31801/cfsuasmas.1019458","DOIUrl":null,"url":null,"abstract":"The full transformation semigroup TnTn is defined to consist of all functions from Xn={1,…,n}Xn={1,…,n} to itself, under the operation of composition. In \\cite{JMH1}, for any αα in TnTn, Howie defined and denoted collapse by c(α)=⋃t∈\\im(α){tα−1:|tα−1|≥2}c(α)=⋃t∈\\im(α){tα−1:|tα−1|≥2}. Let OnOn be the semigroup of all order-preserving transformations and CnCn be the semigroup of all order-preserving and decreasing transformations on XnXn=under its natural order, respectively. \nLet E(On)E(On) be the set of all idempotent elements of OnOn, E(Cn)E(Cn) and N(Cn)N(Cn) be the sets of all idempotent and nilpotent elements of CnCn, respectively. Let UU be one of {Cn,N(Cn),E(Cn),On,E(On)}{Cn,N(Cn),E(Cn),On,E(On)}. For α∈Uα∈U, we consider the set\n\\imc(α)={t∈\\im(α):|tα−1|≥2}\\imc(α)={t∈\\im(α):|tα−1|≥2}. For positive integers 2≤k≤r≤n2≤k≤r≤n, we define\nU(k)={α∈U:t∈\\imc(α) and |tα−1|=k},U(k,r)={α∈U(k):∣∣⋃t∈\\imc(α)tα−1|=r}.U(k)={α∈U:t∈\\imc(α) and |tα−1|=k},U(k,r)={α∈U(k):|⋃t∈\\imc(α)tα−1|=r}.\nThe main objective of this paper is to determine |U(k,r)||U(k,r)|, and so |U(k)||U(k)| for some values rr and kk.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Combinatorial results of collapse for order-preserving and order-decreasing transformations\",\"authors\":\"E. Korkmaz\",\"doi\":\"10.31801/cfsuasmas.1019458\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The full transformation semigroup TnTn is defined to consist of all functions from Xn={1,…,n}Xn={1,…,n} to itself, under the operation of composition. In \\\\cite{JMH1}, for any αα in TnTn, Howie defined and denoted collapse by c(α)=⋃t∈\\\\im(α){tα−1:|tα−1|≥2}c(α)=⋃t∈\\\\im(α){tα−1:|tα−1|≥2}. Let OnOn be the semigroup of all order-preserving transformations and CnCn be the semigroup of all order-preserving and decreasing transformations on XnXn=under its natural order, respectively. \\nLet E(On)E(On) be the set of all idempotent elements of OnOn, E(Cn)E(Cn) and N(Cn)N(Cn) be the sets of all idempotent and nilpotent elements of CnCn, respectively. Let UU be one of {Cn,N(Cn),E(Cn),On,E(On)}{Cn,N(Cn),E(Cn),On,E(On)}. For α∈Uα∈U, we consider the set\\n\\\\imc(α)={t∈\\\\im(α):|tα−1|≥2}\\\\imc(α)={t∈\\\\im(α):|tα−1|≥2}. For positive integers 2≤k≤r≤n2≤k≤r≤n, we define\\nU(k)={α∈U:t∈\\\\imc(α) and |tα−1|=k},U(k,r)={α∈U(k):∣∣⋃t∈\\\\imc(α)tα−1|=r}.U(k)={α∈U:t∈\\\\imc(α) and |tα−1|=k},U(k,r)={α∈U(k):|⋃t∈\\\\imc(α)tα−1|=r}.\\nThe main objective of this paper is to determine |U(k,r)||U(k,r)|, and so |U(k)||U(k)| for some values rr and kk.\",\"PeriodicalId\":44692,\"journal\":{\"name\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31801/cfsuasmas.1019458\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31801/cfsuasmas.1019458","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

全变换半群TnTn被定义为由Xn={1,…,n}Xn={1,……,n}到其自身的所有函数组成,在复合运算下。在{JMH1}中,对于TnTn中的任何αα,Howie定义并表示坍缩为c(α)=⋃t∈\im(α){tα−1:|tα−1|≥2}c(α。设OnOn是所有保序变换的半群,CnCn是XnXn=上所有保序和递减变换在其自然阶下的半群。设E(On)E(On)是OnOn的所有幂等元的集合,E(Cn)E(Cn)和N(Cn,N)分别是CnCn的所有幂等元和幂零元的集合。设UU为{Cn,N(Cn),E(Cn。对于α∈U,我们考虑集\imc(α)={t∈\im(α):|tα−1|≥2}\imc。对于2≤k≤r≤n2≤k≤r≤n的正整数,我们定义U(k)={α∈U:t∈\imc(α)和|tα−1|=k},U(k,r)={(α)tα−1|=r}。本文的主要目的是确定某些值rr和kk的|U(k,r)||U。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Combinatorial results of collapse for order-preserving and order-decreasing transformations
The full transformation semigroup TnTn is defined to consist of all functions from Xn={1,…,n}Xn={1,…,n} to itself, under the operation of composition. In \cite{JMH1}, for any αα in TnTn, Howie defined and denoted collapse by c(α)=⋃t∈\im(α){tα−1:|tα−1|≥2}c(α)=⋃t∈\im(α){tα−1:|tα−1|≥2}. Let OnOn be the semigroup of all order-preserving transformations and CnCn be the semigroup of all order-preserving and decreasing transformations on XnXn=under its natural order, respectively. Let E(On)E(On) be the set of all idempotent elements of OnOn, E(Cn)E(Cn) and N(Cn)N(Cn) be the sets of all idempotent and nilpotent elements of CnCn, respectively. Let UU be one of {Cn,N(Cn),E(Cn),On,E(On)}{Cn,N(Cn),E(Cn),On,E(On)}. For α∈Uα∈U, we consider the set \imc(α)={t∈\im(α):|tα−1|≥2}\imc(α)={t∈\im(α):|tα−1|≥2}. For positive integers 2≤k≤r≤n2≤k≤r≤n, we define U(k)={α∈U:t∈\imc(α) and |tα−1|=k},U(k,r)={α∈U(k):∣∣⋃t∈\imc(α)tα−1|=r}.U(k)={α∈U:t∈\imc(α) and |tα−1|=k},U(k,r)={α∈U(k):|⋃t∈\imc(α)tα−1|=r}. The main objective of this paper is to determine |U(k,r)||U(k,r)|, and so |U(k)||U(k)| for some values rr and kk.
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
自引率
0.00%
发文量
61
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信