{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T11:01:48Z","timestamp":1780743708411,"version":"3.54.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Combinatorics","license":[{"start":{"date-parts":[[2018,11,9]],"date-time":"2018-11-09T00:00:00Z","timestamp":1541721600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2018,11,9]],"date-time":"2018-11-09T00:00:00Z","timestamp":1541721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2018,11,9]],"date-time":"2018-11-09T00:00:00Z","timestamp":1541721600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Rectangulations are partitions of a square into axis-aligned rectangles. A number of results provide bijections between combinatorial equivalence classes of rectangulations and families of pattern-avoiding permutations. Other results deal with local changes involving a single edge of a rectangulation, referred to as flips, edge rotations, or edge pivoting. Such operations induce a graph on equivalence classes of rectangulations, related to so-called flip graphs on triangulations and other families of geometric partitions. In this note, we consider a family of flip operations on the equivalence classes of diagonal rectangulations, and their interpretation as transpositions in the associated Baxter permutations, avoiding the vincular patterns { 3{14}2, 2{41}3 }. This complements results from Law and Reading (JCTA, 2012) and provides a complete characterization of flip operations on diagonal rectangulations, in both geometric and combinatorial terms.<\/jats:p>","DOI":"10.23638\/dmtcs-20-2-14","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:48:59Z","timestamp":1743698939000},"source":"Crossref","is-referenced-by-count":1,"title":["A Note on Flips in Diagonal Rectangulations"],"prefix":"10.23638","volume":"vol. 20 no. 2","author":[{"given":"Jean","family":"Cardinal","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0203-256X","authenticated-orcid":false,"given":"Vera","family":"Sacrist\u00e1n","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rodrigo I.","family":"Silveira","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"25203","published-online":{"date-parts":[[2018,11,9]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1712.07919v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1712.07919v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:48:59Z","timestamp":1743698939000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/4315"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,9]]},"references-count":0,"journal-issue":{"issue":"Combinatorics","published-online":{"date-parts":[[2018,11,9]]}},"URL":"https:\/\/doi.org\/10.23638\/dmtcs-20-2-14","relation":{"has-preprint":[{"id-type":"arxiv","id":"1712.07919v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1712.07919v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1712.07919","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1712.07919","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"value":"1365-8050","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,9]]},"article-number":"4315"}}