{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T09:07:13Z","timestamp":1768295233638,"version":"3.49.0"},"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>Simultaneous core partitions have attracted much attention since Anderson's work on the number of $(t_1,t_2)$-core partitions. In this paper we focus on simultaneous core partitions with distinct parts. The generating function of $t$-core partitions with distinct parts is obtained. We also prove results on the number, the largest size and the average size of $(t, t + 1)$-core partitions with distinct parts. This gives a complete answer to a conjecture of Amdeberhan, which is partly and independently proved by Straub, Nath and Sellers, and Zaleski recently.<\/jats:p>","DOI":"10.37236\/6907","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:37:01Z","timestamp":1578670621000},"source":"Crossref","is-referenced-by-count":6,"title":["Core Partitions with Distinct Parts"],"prefix":"10.37236","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9906-4765","authenticated-orcid":false,"given":"Huan","family":"Xiong","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,3,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p57\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p57\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:37:43Z","timestamp":1579235863000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p57"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/6907","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,7]]},"article-number":"P1.57"}}