{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:12Z","timestamp":1753893792371,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>An inversion sequence of length $n$ is a sequence of integers $e=e_1\\cdots\u00a0 e_n$ which satisfies for each $i\\in[n]=\\{1,2,\\ldots,n\\}$ the inequality $0\\le e_i &lt; i$. For a set of patterns $P$, we let $\\mathbf{I}_n(P)$ denote the set of inversion sequences of length $n$ that avoid all the patterns from~$P$. We say that two sets of patterns $P$ and $Q$ are I-Wilf-equivalent if $|\\mathbf{I}_n(P)|=|\\mathbf{I}_n(Q)|$ for every~$n$. In this paper, we show that the number of I-Wilf-equivalence classes among triples of length-3 patterns is $137$, $138$ or~$139$. In particular, to show that this number is exactly $137$, it remains to prove $\\{101,102,110\\}\\stackrel{\\mathbf{I}}{\\sim}\\{021,100,101\\}$ and $\\{100,110,201\\}\\stackrel{\\mathbf{I}}{\\sim}\\{100,120,210\\}$.<\/jats:p>","DOI":"10.37236\/11603","type":"journal-article","created":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T08:37:20Z","timestamp":1691743040000},"source":"Crossref","is-referenced-by-count":0,"title":["Inversion Sequences Avoiding a Triple of Patterns of 3 Letters"],"prefix":"10.37236","volume":"30","author":[{"given":"David","family":"Callan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V\u00edt","family":"Jel\u00ednek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toufik","family":"Mansour","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2023,8,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p19\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i3p19\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T08:37:37Z","timestamp":1691743057000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i3p19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,11]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/11603","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,8,11]]},"article-number":"P3.19"}}