{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:27Z","timestamp":1753889907016,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Combinatorics","license":[{"start":{"date-parts":[[2018,10,24]],"date-time":"2018-10-24T00:00:00Z","timestamp":1540339200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2018,10,24]],"date-time":"2018-10-24T00:00:00Z","timestamp":1540339200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2018,10,24]],"date-time":"2018-10-24T00:00:00Z","timestamp":1540339200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"name":"National Science Foundation","award":["1358659"],"award-info":[{"award-number":["1358659"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We present two families of Wilf-equivalences for consecutive and quasi-consecutive vincular patterns. These give new proofs of the classification of consecutive patterns of length $4$ and $5$. We then prove additional equivalences to explicitly classify all quasi-consecutive patterns of length $5$ into 26 Wilf-equivalence classes.<\/jats:p><jats:p>Comment: 20 pages. Reformatted for DMTCS overlay journal<\/jats:p>","DOI":"10.23638\/dmtcs-20-2-12","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:46:43Z","timestamp":1743698803000},"source":"Crossref","is-referenced-by-count":0,"title":["The 26 Wilf-equivalence classes of length five quasi-consecutive patterns"],"prefix":"10.23638","volume":"vol. 20 no. 2","author":[{"given":"Evan","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shyam","family":"Narayanan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2018,10,24]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1609.04626v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1609.04626v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:46:43Z","timestamp":1743698803000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/4030"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,24]]},"references-count":0,"journal-issue":{"issue":"Combinatorics","published-online":{"date-parts":[[2018,10,24]]}},"URL":"https:\/\/doi.org\/10.23638\/dmtcs-20-2-12","relation":{"has-preprint":[{"id-type":"arxiv","id":"1609.04626v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1609.04626v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1609.04626","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1609.04626","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2018,10,24]]},"article-number":"4030"}}