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dc.contributor.authorWang, Victor Y.
dc.date.accessioned2016-06-07T15:51:10Z
dc.date.available2016-06-07T15:51:10Z
dc.date.issued2016-01
dc.date.submitted2015-08
dc.identifier.issn1097-1440
dc.identifier.issn1077-8926
dc.identifier.urihttp://hdl.handle.net/1721.1/103038
dc.description.abstractFix coprime s; t > 1. We re-prove, without Ehrhart reciprocity, a conjecture of Armstrong (recently verified by Johnson) that the definitely many simultaneous (s; t)- cores have average size 1 24 (s - 1)(t - 1)(s+t+1), and that the subset of self-conjugate cores has the same average (first shown by Chen{Huang{Wang). We similarly prove a recent conjecture of Fayers that the average weighted by an inverse stabilizer| giving the \expected size of the t-core of a random s-core"|is 1 24 (s - 1)(t2 - 1). We also prove Fayers' conjecture that the analogous self-conjugate average is the same if t is odd, but instead 1 24 (s - 1)(t2 + 2) if t is even. In principle, our explicit methods|or implicit variants thereof|extend to averages of arbitrary powers. The main new observation is that the stabilizers appearing in Fayers' conjectures have simple formulas in Johnson's z-coordinates parameterization of (s; t)-cores. We also observe that the z-coordinates extend to parameterize general t-cores. As an example application with t := s+d, we count the number of (s; s+d; s+2d)- cores for coprime s; d > 1, verifying a recent conjecture of Amdeberhan and Leven.en_US
dc.language.isoen_US
dc.publisherEuropean Mathematical Information Service (EMIS)en_US
dc.relation.isversionofhttp://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i1p4en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceEuropean Mathematical Information Service (EMIS)en_US
dc.titleSimultaneous Core Partitions: Parameterizations and Sumsen_US
dc.typeArticleen_US
dc.identifier.citationWang, Victor Y. "Simultaneous Core Partitions: Parameterizations and Sums." Electronic Journal of Combinatorics 23(1) (2016), p.1-4.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorWang, Victor Y.en_US
dc.relation.journalElectronic Journal of Combinatoricsen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsWang, Victor Y.en_US
dspace.embargo.termsNen_US
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


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