{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,6]],"date-time":"2026-06-06T11:01:55Z","timestamp":1780743715999,"version":"3.54.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We provide a new succession rule (i.e. generating tree) associated with Schr\u00f6der numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schr\u00f6der and Baxter generalizations of parallelogram polyominoes, called slicings, which grow according to these succession rules. In passing, we also exhibit Schr\u00f6der subclasses of Baxter classes, namely a Schr\u00f6der subset of triples of non-intersecting lattice paths, a new Schr\u00f6der subset of Baxter permutations, and a new Schr\u00f6der subset of mosaic floorplans. Finally, we define two families of subclasses of Baxter slicings: the $m$-skinny slicings and the $m$-row-restricted slicings, for $m \\in \\mathbb{N}$. Using functional equations and the kernel method, their generating functions are computed in some special cases, and we conjecture that they are algebraic for any $m$.<\/jats:p>","DOI":"10.37236\/7375","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:05:09Z","timestamp":1578639909000},"source":"Crossref","is-referenced-by-count":5,"title":["Slicings of Parallelogram Polyominoes: Catalan, Schr\u00f6der, Baxter, and Other Sequences"],"prefix":"10.37236","volume":"26","author":[{"given":"Nicholas R.","family":"Beaton","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mathilde","family":"Bouvel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Veronica","family":"Guerrini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simone","family":"Rinaldi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2019,7,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p13\/7873","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i3p13\/7873","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:11:19Z","timestamp":1579234279000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i3p13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,19]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,7,4]]}},"URL":"https:\/\/doi.org\/10.37236\/7375","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,19]]},"article-number":"P3.13"}}