منابع مشابه
Differential Operators, Shifted Parts, and Hook Lengths
We discuss Sekiguchi-type differential operators, their eigenvalues, and a generalization of Andrews-Goulden-Jackson formula. These will be applied to extract explicit formulae involving shifted partitions and hook lengths. 1. Differential operators. The standard Jack symmetric polynomials Pλ(y1, . . . , yn;α) (see Macdoland, Stanley [5, 10]) as well as their shifted counter-parts (replace θ = ...
متن کاملSymmetric Group Character Degrees and Hook Numbers
In this article we prove the following result: that for any two natural numbers k and `, and for all sufficiently large symmetric groups Sn, there are k disjoint sets of ` irreducible characters of Sn, such that each set consists of characters with the same degree, and distinct sets have different degrees. In particular, this resolves a conjecture most recently made by Moretó in [5]. The method...
متن کاملAsymptotics of Young Diagrams and Hook Numbers
Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition μ, we deduce several skew diagrams which are related to μ. To each such skew diagram there corresponds the product of its hook numbers. By asymptotic methods we obtain some unexpected arithmetic properties between these products. The authors do not kno...
متن کاملThe Weighted Hook Length Formula III: Shifted Tableaux
Recently, a simple proof of the hook length formula was given via the branching rule. In this paper, we extend the results to shifted tableaux. We give a bijective proof of the branching rule for the hook lengths for shifted tableaux; present variants of this rule, including weighted versions; and make the first tentative steps toward a bijective proof of the hook length formula for d-complete ...
متن کاملSwiching Rule on the Shifted Rim Hook Tableaux
When the Schur function sλ corresponding to a partition λ is defined as the generating function of the column strict tableaux of shape λ it is not at all obvious that sλ is symmetric. In [BK] Bender and Knuth showed that sλ is symmetric by describing a switching rule for column strict tableaux, which is essentially equivalent to the jeu de taquin of Schützenberger (see [Sü]). Bender and Knuth’s...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90030-l