{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:22:03Z","timestamp":1759335723227,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In 2007, Olsson and Stanton gave an explicit form for the largest $(a, b)$-core partition, for any relatively prime positive integers $a$ and $b$, and asked whether there exists an $(a, b)$-core that contains all other $(a, b)$-cores as subpartitions; this question was answered in the affirmative first by Vandehey and later by Fayers independently. In this paper we investigate a generalization of this question, which was originally posed by Fayers: for what triples of positive integers $(a, b, c)$ does there exist an $(a, b, c)$-core that contains all other $(a, b, c)$-cores as subpartitions? We completely answer this question when $a$, $b$, and $c$ are pairwise relatively prime; we then use this to generalize the result of Olsson and Stanton.<\/jats:p>","DOI":"10.37236\/4773","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T18:57:14Z","timestamp":1578682634000},"source":"Crossref","is-referenced-by-count":2,"title":["When Does the Set of $(a, b, c)$-Core Partitions Have a Unique Maximal Element?"],"prefix":"10.37236","volume":"22","author":[{"given":"Amol","family":"Aggarwal","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,5,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:17:02Z","timestamp":1579238222000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i2p31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,22]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/4773","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,5,22]]},"article-number":"P2.31"}}