{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T06:25:54Z","timestamp":1770359154994,"version":"3.49.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper we present a bijection between composition matrices and ($\\mathbf{2+2}$)-free posets.  This bijection maps partition matrices to factorial posets, and induces a bijection from upper triangular matrices with non-negative entries having no rows or columns of zeros to unlabeled ($\\mathbf{2+2}$)-free posets.  Chains in a ($\\mathbf{2+2}$)-free poset are shown to correspond to entries in the associated composition matrix whose hooks satisfy a simple condition. It is shown that the action of taking the dual of a poset corresponds to reflecting the associated composition matrix in its anti-diagonal. We further characterize posets which are both ($\\mathbf{2+2}$)- and ($\\mathbf{3+1}$)-free by certain properties of their associated composition matrices.<\/jats:p>","DOI":"10.37236\/531","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:53:14Z","timestamp":1578714794000},"source":"Crossref","is-referenced-by-count":9,"title":["Composition Matrices, (2+2)-Free Posets and their Specializations"],"prefix":"10.37236","volume":"18","author":[{"given":"Mark","family":"Dukes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V\u00edt","family":"Jel\u00ednek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martina","family":"Kubitzke","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,2,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p44\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p44\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:16:12Z","timestamp":1579302972000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/531","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2,21]]},"article-number":"P44"}}