{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:19:35Z","timestamp":1759335575874,"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>Determining if a symmetric function is Schur-positive is a prevalent and, in general, a notoriously difficult problem.\u00a0 In this paper we study the Schur-positivity of a family of symmetric functions.\u00a0 Given a partition $\\nu$, we denote by $\\nu^c$ its complement in a square partition $(m^m)$.\u00a0\u00a0 We conjecture a\u00a0 Schur-positivity criterion\u00a0 for symmetric functions of the form $s_{\\mu'}s_{\\mu^c}-s_{\\nu'}s_{\\nu^c}$, where $\\nu$ is a partition of weight $|\\mu|-1$ contained in $\\mu$ and the complement of $\\mu$ is taken in the same square partition as the complement of $\\nu$. We prove the conjecture in many cases.<\/jats:p>","DOI":"10.37236\/3796","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:54:38Z","timestamp":1578704078000},"source":"Crossref","is-referenced-by-count":2,"title":["Schur-Positivity in a Square"],"prefix":"10.37236","volume":"21","author":[{"given":"Cristina","family":"Ballantine","sequence":"first","affiliation":[]},{"given":"Rosa","family":"Orellana","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,9,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p46\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:44:08Z","timestamp":1579257848000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i3p46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,25]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,7,3]]}},"URL":"https:\/\/doi.org\/10.37236\/3796","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,9,25]]},"article-number":"P3.46"}}