{"title":"论范围为区间的有限链的保阶变换一元体","authors":"Vítor H. Fernandes","doi":"10.1007/s00233-024-10466-2","DOIUrl":null,"url":null,"abstract":"<p>We give a presentation for the monoid <span>\\(\\mathscr{I}\\mathscr{O}_n\\)</span> of all order-preserving transformations of an <i>n</i>-chain whose ranges are intervals. We also consider the submonoid <span>\\(\\mathscr{I}\\mathscr{O}_n^-\\)</span> of <span>\\(\\mathscr{I}\\mathscr{O}_n\\)</span> consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the monoid of order-preserving transformations of a finite chain whose ranges are intervals\",\"authors\":\"Vítor H. Fernandes\",\"doi\":\"10.1007/s00233-024-10466-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We give a presentation for the monoid <span>\\\\(\\\\mathscr{I}\\\\mathscr{O}_n\\\\)</span> of all order-preserving transformations of an <i>n</i>-chain whose ranges are intervals. We also consider the submonoid <span>\\\\(\\\\mathscr{I}\\\\mathscr{O}_n^-\\\\)</span> of <span>\\\\(\\\\mathscr{I}\\\\mathscr{O}_n\\\\)</span> consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00233-024-10466-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00233-024-10466-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们给出了范围为区间的 n 链的所有保序变换的单元 \(\mathscr{I}\mathscr{O}_n\)。我们还考虑了 \(\mathscr{I}\mathscr{O}_n^-\) 的子单体 \(\mathscr{I}\mathscr{O}_n\)，这个子单体由阶递减变换组成，我们确定了它的心数、秩和呈现方式。
On the monoid of order-preserving transformations of a finite chain whose ranges are intervals
We give a presentation for the monoid \(\mathscr{I}\mathscr{O}_n\) of all order-preserving transformations of an n-chain whose ranges are intervals. We also consider the submonoid \(\mathscr{I}\mathscr{O}_n^-\) of \(\mathscr{I}\mathscr{O}_n\) consisting of order-decreasing transformations, for which we determine the cardinality, the rank and a presentation.
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