dc.contributor.author | Stanley, Richard P. | |
dc.date.accessioned | 2011-02-01T13:43:05Z | |
dc.date.available | 2011-02-01T13:43:05Z | |
dc.date.issued | 2009-10 | |
dc.identifier.issn | 1382-4090 | |
dc.identifier.issn | 1572-9303 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/60871 | |
dc.description.abstract | The main result of this paper is a generalization of a conjecture of Guoniu Han, originally inspired by an identity of Nekrasov and Okounkov. Our result states that if F is any symmetric function (say over ℚ) and if
$$\Phi_n(F)=\frac{1}{n!}\sum_{\lambda\vdash n}f_\lambda^2F(h_u^2:u\in\lambda),$$
where h u denotes the hook length of the square u of the partition λ of n and f λ is the number of standard Young tableaux of shape λ, then Φ n (F) is a polynomial function of n. A similar result is obtained when F(h u 2:u∈λ) is replaced with a function that is symmetric separately in the contents c u of λ and the shifted parts λ i +n−i of λ. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (Grant No.0604423) | en_US |
dc.language.iso | en_US | |
dc.publisher | Springer | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/s11139-009-9185-x | en_US |
dc.rights | Attribution-Noncommercial-Share Alike 3.0 Unported | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/ | en_US |
dc.source | MIT web domain | en_US |
dc.title | Some combinatorial properties of hook lengths, contents, and parts of partitions | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Stanley, Richard. “Some combinatorial properties of hook lengths, contents, and parts of partitions.” The Ramanujan Journal 23.1 (2010): 91-105-105. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.approver | Stanley, Richard P. | |
dc.contributor.mitauthor | Stanley, Richard P. | |
dc.relation.journal | Ramanujan Journal | en_US |
dc.eprint.version | Author's final manuscript | |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Stanley, Richard P. | en |
dc.identifier.orcid | https://orcid.org/0000-0003-3123-8241 | |
mit.license | OPEN_ACCESS_POLICY | en_US |
mit.metadata.status | Complete | |