{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821995,"version":"3.41.2"},"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>We define an extension of matroid rank submodularity called  $R$-submodularity, and introduce a minor-closed class of matroids called extended submodular matroids that are well-behaved with respect to $R$-submodularity.  We apply $R$-submodularity to study a class of matroids with negatively correlated multivariate Tutte polynomials called the $Z$-Rayleigh matroids.  First, we show that the class of extended submodular matroids are $Z$-Rayleigh.  Second, we characterize a minor-minimal non-$Z$-Rayleigh matroid using its $R$-submodular properties.  Lastly, we use $R$-submodularity to show that the Fano and non-Fano matroids (neither of which is extended submodular) are $Z$-Rayleigh, thus giving the first known examples of $Z$-Rayleigh matroids without the half-plane property.<\/jats:p>","DOI":"10.37236\/600","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:47:24Z","timestamp":1578714444000},"source":"Crossref","is-referenced-by-count":0,"title":["An Extension of Matroid Rank Submodularity and the $Z$-Rayleigh Property"],"prefix":"10.37236","volume":"18","author":[{"given":"Arun P.","family":"Mani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,5,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p113\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p113\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:11:57Z","timestamp":1579302717000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p113"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5,16]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/600","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,5,16]]},"article-number":"P113"}}