{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T12:33:21Z","timestamp":1772368401884,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A floorplan is a tiling of a rectangle by rectangles.\u00a0There are natural ways to order the elements - rectangles and segments - of a floorplan.\u00a0Ackerman, Barequet and Pinter studied\u00a0a pair of orders induced by\u00a0neighborhood relations between rectangles,\u00a0and obtained a natural bijection between these pairs\u00a0and $(2 - 41 - 3, 3 - 14 - 2)$-avoiding permutations, also\u00a0known as (reduced) Baxter permutations.In the present paper, we first perform a similar study for a pair of\u00a0orders induced by neighborhood relations between segments\u00a0of a floorplan. We obtain a natural bijection between these\u00a0pairs and another family of permutations, namely\u00a0$(2 - 14 - 3, 3 - 41 - 2)$-avoiding permutations.Then, we investigate relations between\u00a0the two kinds of pairs of orders - and, correspondingly, between\u00a0$(2 - 41 - 3, 3 - 14 - 2)$- and $(2 - 14 - 3, 3 - 41 -\u00a02)$-avoiding permutations. In particular, we prove that the\u00a0superposition of both permutations gives a complete Baxter\u00a0permutation (originally called $w$-admissible by Baxter\u00a0and Joichi in the sixties). In other words, $(2 - 14 - 3, 3 - 41 -\u00a02)$-avoiding permutations are the hidden part of complete\u00a0Baxter permutations. We enumerate these permutations.\u00a0To our knowledge, the characterization of these permutations in terms of\u00a0forbidden patterns and their enumeration are both new results.Finally, we also study the special case of\u00a0the\u00a0so-called guillotine floorplans.<\/jats:p>","DOI":"10.37236\/2607","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:32:38Z","timestamp":1578706358000},"source":"Crossref","is-referenced-by-count":8,"title":["Orders Induced by Segments in Floorplans and $(2 - 14 - 3, 3 - 41 - 2)$-Avoiding Permutations"],"prefix":"10.37236","volume":"20","author":[{"given":"Andrei","family":"Asinowski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gill","family":"Barequet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mireille","family":"Bousquet-M\u00e9lou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toufik","family":"Mansour","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ron Y.","family":"Pinter","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2013,5,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p35\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i2p35\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:20:24Z","timestamp":1579260024000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i2p35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,24]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2013,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/2607","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,24]]},"article-number":"P35"}}