Generalized hook lengths in symbols and partitions

Christine Bessenrodt; Jean-Baptiste Gramain; Jørn Børling Olsson

Generalized hook lengths in symbols and partitions

Christine Bessenrodt, Jean-Baptiste Gramain, Jørn Børling Olsson

Institut for Matematiske Fag

4 Citationer (Scopus)

Abstract

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.

Originalsprog	Engelsk
Tidsskrift	Journal of Algebraic Combinatorics
Vol/bind	36
Udgave nummer	2
Sider (fra-til)	309-332
Antal sider	24
ISSN	0925-9899
Status	Udgivet - sep. 2012

Citationsformater

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T1 - Generalized hook lengths in symbols and partitions

AU - Bessenrodt, Christine

AU - Gramain, Jean-Baptiste

AU - Olsson, Jørn Børling

PY - 2012/9

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N2 - 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.

AB - 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.

M3 - Journal article

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EP - 332

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

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Generalized hook lengths in symbols and partitions

Abstract

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Citationsformater