dc.contributor.author | Wang, Victor Y. | |
dc.date.accessioned | 2016-06-07T15:51:10Z | |
dc.date.available | 2016-06-07T15:51:10Z | |
dc.date.issued | 2016-01 | |
dc.date.submitted | 2015-08 | |
dc.identifier.issn | 1097-1440 | |
dc.identifier.issn | 1077-8926 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/103038 | |
dc.description.abstract | Fix 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.iso | en_US | |
dc.publisher | European Mathematical Information Service (EMIS) | en_US |
dc.relation.isversionof | http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i1p4 | en_US |
dc.rights | Article 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.source | European Mathematical Information Service (EMIS) | en_US |
dc.title | Simultaneous Core Partitions: Parameterizations and Sums | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Wang, Victor Y. "Simultaneous Core Partitions: Parameterizations and Sums." Electronic Journal of Combinatorics 23(1) (2016), p.1-4. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Wang, Victor Y. | en_US |
dc.relation.journal | Electronic Journal of Combinatorics | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Wang, Victor Y. | en_US |
dspace.embargo.terms | N | en_US |
mit.license | PUBLISHER_POLICY | en_US |
mit.metadata.status | Complete | |