Geodesic
Generalized hook lengths in symbols and partitions
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 2, pp. 309-332.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 relative hook formula for the degree of characters of the symmetric group discovered by G. Malle and G. Navarro in Trans. Am. Math. Soc. 363, 6647-6669, 2011.
Keywords: symbols, hooks, hook lengths, partitions, core, quotient 
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     title = {Generalized hook lengths in symbols and partitions},
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Bessenrodt, Christine; Gramain, Jean-Baptiste; Olsson, Jørn B. Generalized hook lengths in symbols and partitions. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 2, pp. 309-332. http://geodesic.mathdoc.fr/item/JAC_2012__36_2_a0/