{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:52:28Z","timestamp":1753894348701,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Permutation Patterns","license":[{"start":{"date-parts":[[2016,7,21]],"date-time":"2016-07-21T00:00:00Z","timestamp":1469059200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We investigate pattern avoidance in permutations satisfying some additional\nrestrictions. These are naturally considered in terms of avoiding patterns in\nlinear extensions of certain forest-like partially ordered sets, which we call\nbinary shrub forests. In this context, we enumerate forests avoiding patterns\nof length three. In four of the five non-equivalent cases, we present explicit\nenumerations by exhibiting bijections with certain lattice paths bounded above\nby the line $y=\\ell x$, for some $\\ell\\in\\mathbb{Q}^+$, one of these being the\ncelebrated Duchon's club paths with $\\ell=2\/3$. In the remaining case, we use\nthe machinery of analytic combinatorics to determine the minimal polynomial of\nits generating function, and deduce its growth rate.<\/jats:p>","DOI":"10.46298\/dmtcs.1322","type":"journal-article","created":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T21:53:48Z","timestamp":1629755628000},"source":"Crossref","is-referenced-by-count":0,"title":["Pattern avoidance in forests of binary shrubs"],"prefix":"10.46298","volume":"Vol. 18 no. 2, Permutation...","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7179-2285","authenticated-orcid":false,"given":"David","family":"Bevan","sequence":"first","affiliation":[]},{"given":"Derek","family":"Levin","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3389-0586","authenticated-orcid":false,"given":"Peter","family":"Nugent","sequence":"additional","affiliation":[]},{"given":"Jay","family":"Pantone","sequence":"additional","affiliation":[]},{"given":"Lara","family":"Pudwell","sequence":"additional","affiliation":[]},{"given":"Manda","family":"Riehl","sequence":"additional","affiliation":[]},{"given":"ML","family":"Tlachac","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2016,7,21]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dmtcs.episciences.org\/1541\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dmtcs.episciences.org\/1541\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:11:50Z","timestamp":1687291910000},"score":1,"resource":{"primary":{"URL":"https:\/\/dmtcs.episciences.org\/1322"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,21]]},"references-count":0,"journal-issue":{"issue":"Permutation Patterns","published-online":{"date-parts":[[2016,7,21]]}},"URL":"https:\/\/doi.org\/10.46298\/dmtcs.1322","relation":{"has-preprint":[{"id-type":"arxiv","id":"1510.08036v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1510.08036v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1510.08036","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1510.08036","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2016,7,21]]},"article-number":"1322"}}