{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T11:23:44Z","timestamp":1758281024003,"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>We prove generalized arithmetic-geometric mean inequalities for quasi-means arising from symmetric polynomials. The inequalities are satisfied by all positive, homogeneous symmetric polynomials, as well as a certain family of non-homogeneous polynomials; this family allows us to prove the following combinatorial result for marked square grids.Suppose that the cells of a $n \\times n$ checkerboard are each independently filled or empty, where the probability that a cell is filled depends only on its column. We prove that for any $0 \\leq \\ell \\leq n$, the probability that each column has at most $\\ell$ filled sites is less than or equal to the probability that each row has at most $\\ell$ filled sites.<\/jats:p>","DOI":"10.37236\/2915","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:22:32Z","timestamp":1578687752000},"source":"Crossref","is-referenced-by-count":1,"title":["Symmetric Polynomials and Symmetric Mean Inequalities"],"prefix":"10.37236","volume":"20","author":[{"given":"Karl","family":"Mahlburg","sequence":"first","affiliation":[]},{"given":"Clifford","family":"Smyth","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,9,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T06:13:48Z","timestamp":1579241628000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i3p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,6]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2013,7,19]]}},"URL":"https:\/\/doi.org\/10.37236\/2915","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,9,6]]},"article-number":"P34"}}