{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:52Z","timestamp":1753893832580,"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 provide several classes of examples to show that Stanley's plethysm conjecture and a reformulation by Pylyavskyy, both concerning the ranks of certain matrices $K^{\\lambda}$ associated with Young diagrams $\\lambda$, are in general false. We also provide bounds on the rank of $K^{\\lambda}$ by which it may be possible to show that the approach of Black and List to Foulkes' conjecture does not work in general. Finally, since Black and List's work concerns $K^{\\lambda}$ for rectangular shapes $\\lambda$, we suggest a constructive way to prove that $K^{\\lambda}$ does not have full rank when $\\lambda$ is a large rectangle.<\/jats:p>","DOI":"10.37236\/1050","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:03:16Z","timestamp":1578700996000},"source":"Crossref","is-referenced-by-count":1,"title":["Some Plethysm Results related to Foulkes' Conjecture"],"prefix":"10.37236","volume":"13","author":[{"given":"Steven","family":"Sivek","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,3,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:18:01Z","timestamp":1579303081000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1050","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,3,14]]},"article-number":"R24"}}