{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T22:30:27Z","timestamp":1784068227861,"version":"3.55.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>An ascent sequence is a sequence $a_1a_2\\cdots a_n$ consisting of non-negative integers satisfying $a_1=0$ and for $1&lt;i\\leq n$, $a_i\\leq \\text{asc}(a_1a_2\\cdots a_{i-1})+1$, where $\\text{asc}(a_1a_2\\cdots a_k)$ is the number of ascents in the sequence $a_1a_2\\cdots a_k$. We say that two sets of patterns $B$ and $C$ are $A$-Wilf-equivalent if the number of ascent sequences of length $n$ that avoid $B$ equals the number of ascent sequences of length $n$ that avoid $C$, for all $n\\geq0$. In this paper, we show that the number of $A$-Wilf-equivalences among triples of length-3 patterns is 62. The main tool is generating trees; bijective methods are also sometimes used. One case is of particular interest: ascent sequences avoiding the 3 patterns 100, 201 and 210 are easy to characterize, but it seems remarkably involved to show that, like 021-avoiding ascent sequences, they are counted by the Catalan numbers.<\/jats:p>","DOI":"10.37236\/12720","type":"journal-article","created":{"date-parts":[[2025,3,16]],"date-time":"2025-03-16T21:22:17Z","timestamp":1742160137000},"source":"Crossref","is-referenced-by-count":1,"title":["Ascent Sequences Avoiding a Triple of Length-3 Patterns"],"prefix":"10.37236","volume":"32","author":[{"given":"David","family":"Callan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Toufik","family":"Mansour","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2025,3,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i1p40\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i1p40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,16]],"date-time":"2025-03-16T21:22:17Z","timestamp":1742160137000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i1p40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1,17]]}},"URL":"https:\/\/doi.org\/10.37236\/12720","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,14]]},"article-number":"P1.40"}}