{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T08:49:59Z","timestamp":1768294199906,"version":"3.49.0"},"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 apply lattice point techniques to the study of simultaneous core partitions. Our central observation is that for $a$ and $b$ relatively prime, the abacus construction identifies the set of simultaneous $(a,b)$-core partitions with lattice points in a rational simplex. We apply this result in two main ways: using Ehrhart theory, we reprove Anderson's theorem that there are $(a+b-1)!\/a!b!$ simultaneous $(a,b)$-cores; and using Euler-Maclaurin theory we prove Armstrong's conjecture that the average size of an $(a,b)$-core is $(a+b+1)(a-1)(b-1)\/24$. Our methods also give new derivations of analogous formulas for the number and average size of self-conjugate $(a,b)$-cores.<\/jats:p>","DOI":"10.37236\/5734","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:10:09Z","timestamp":1578651009000},"source":"Crossref","is-referenced-by-count":11,"title":["Lattice Points and Simultaneous Core Partitions"],"prefix":"10.37236","volume":"25","author":[{"given":"Paul","family":"Johnson","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,9,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p47\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p47\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:26:11Z","timestamp":1579217171000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i3p47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,21]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/5734","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9,21]]},"article-number":"P3.47"}}