On multisets of hook lengths of partitions
نویسندگان
چکیده
منابع مشابه
Generalized Hook Lengths in Symbols and Partitions
In this paper we present, for any integer d, a description of the set of hooks in a d-symbol. We then introduce generalized hook length functions for a d-symbol, and prove a general result about them, involving the core and quotient of the symbol. We list some applications, for example to the well-known hook lengths in integer partitions. This leads in particular to a generalization of a relati...
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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
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Citation Stanley, Richard. " Some combinatorial properties of hook lengths, contents, and parts of partitions. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. 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 state...
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Recently, the first author generalized a formula of Nekrasov and Okounkov which gives a combinatorial formula, in terms of hook lengths of partitions, for the coefficients of certain power series. In the course of this investigation, he conjectured that a(n) = 0 if and only if b(n) = 0, where integers a(n) and b(n) are defined by
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The nonsymmetric Jack polynomials are defined to be the simultaneous eigenfunctions of a parametrized commuting set of first-order differentialdifference operators. These polynomials form a basis for the homogeneous polynomials and they are labeled by compositions, just like the monomials. The coefficients of the polynomials when expanded in the standard monomial basis are rational functions of...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2013
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.08.021