{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T00:33:27Z","timestamp":1778286807613,"version":"3.51.4"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We investigate permutations and involutions that avoid a pattern of length three and have a unique longest increasing subsequence (ULIS). We prove an explicit formula for 231-avoiders, we show that the growth rate for 321-avoiding permutations with a ULIS is 4, and prove that their generating function is not rational. We relate the case of 132-avoiders to the existing literature, raising some interesting questions. For involutions, we construct a bijection between 132-avoiding involutions with a ULIS and bidirectional ballot sequences.<\/jats:p>","DOI":"10.37236\/9506","type":"journal-article","created":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T08:21:33Z","timestamp":1608020493000},"source":"Crossref","is-referenced-by-count":1,"title":["Pattern Avoiding Permutations with a Unique Longest Increasing Subsequence"],"prefix":"10.37236","volume":"27","author":[{"given":"Mikl\u00f3s","family":"B\u00f3na","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elijah","family":"DeJonge","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,12,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p44\/8225","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p44\/8225","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T08:21:33Z","timestamp":1608020493000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,11]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/9506","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,11]]},"article-number":"P4.44"}}