{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:20:22Z","timestamp":1759335622047,"version":"3.41.2"},"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>The symmetry of the joint distribution of the numbers of crossings and nestings of length $2$ has been observed in many\u00a0 combinatorial structures, including permutations, matchings, set partitions, linked partitions, and certain families of graphs.\u00a0 These results have been unified in the larger context of enumeration of northeast and southeast chains of length $2$ in $01$-fillings of moon polyominoes. In this paper\u00a0 we extend this symmetry to fillings of a more general family\u2014layer polyominoes, which are intersection-free and row-convex, but not necessarily column-convex.\u00a0 Our main result is that the joint distribution of the numbers of northeast\u00a0 and southeast chains of length $2$ over $01$-fillings is symmetric and invariant under an arbitrary permutation of rows. <\/jats:p>","DOI":"10.37236\/3291","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:21:46Z","timestamp":1578705706000},"source":"Crossref","is-referenced-by-count":2,"title":["Chains of Length 2 in Fillings of Layer Polyominoes"],"prefix":"10.37236","volume":"20","author":[{"given":"Mitch","family":"Phillipson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Catherine H.","family":"Yan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean","family":"Yeh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2013,9,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p51\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:12:39Z","timestamp":1579259559000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i3p51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,26]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2013,7,19]]}},"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.37236\/3291","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,9,26]]},"article-number":"P51"}}