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.
Original language | English |
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Pages (from-to) | 309-332 |
Number of pages | 24 |
Journal | Journal of Algebraic Combinatorics |
Volume | 36 |
Issue number | 2 |
Early online date | 8 Dec 2011 |
DOIs | |
Publication status | Published - Sept 2012 |
Keywords
- symbols
- hooks
- hook lengths
- partitions
- core
- quotient