Some combinatorial properties of hook lengths, contents, and parts of partitions
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Stanley_Some Combinatorial.pdf
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162.64 KB
Format
Adobe PDF
Checksum (MD5)
a76b04dc8f1913cd2c3f45337a630fcc
Author(s)
Stanley, Richard P.
Date Issued
October 2009
Journal
Ramanujan Journal
Publisher
Springer
Citation
Stanley, Richard. “Some combinatorial properties of hook lengths, contents, and parts of partitions.” The Ramanujan Journal 23.1 (2010): 91-105-105.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Attribution-Noncommercial-Share Alike 3.0 Unported
Persistent DSpace Link
DOI of Published Version
http://dx.doi.org/10.1007/s11139-009-9185-x
