{"title":"Longest and shortest factorizations in embedding dimension three","authors":"Baian Liu, JiaYan Yap","doi":"10.2140/involve.2023.16.673","DOIUrl":null,"url":null,"abstract":"For a numerical monoid $\\langle n_1, \\dots, n_k \\rangle$ minimally generated by $n_1, \\dots, n_k \\in \\mathbb{N}$ with $n_1<\\cdots<n_k$, the longest and shortest factorization lengths of an element $x$, denoted as $L(x)$ and $\\ell(x)$, respectively, follow the identities $L(x+n_1) = L(x) + 1$ and $\\ell(x+n_k) = \\ell(x) + 1$ for sufficiently large elements $x$. We characterize when these identities hold for all elements of numerical monoids of embedding dimension three.","PeriodicalId":36396,"journal":{"name":"Involve","volume":"74 ","pages":"0"},"PeriodicalIF":0.2000,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Involve","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/involve.2023.16.673","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
For a numerical monoid $\langle n_1, \dots, n_k \rangle$ minimally generated by $n_1, \dots, n_k \in \mathbb{N}$ with $n_1<\cdots