Generalized hook lengths in symbols and partitions
Combinatorics
2013-01-09 v1 Representation Theory
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 [3].
Cite
@article{arxiv.1101.5067,
title = {Generalized hook lengths in symbols and partitions},
author = {Christine Bessenrodt and Jorn B. Olsson and Jean-Baptiste Gramain},
journal= {arXiv preprint arXiv:1101.5067},
year = {2013}
}