Generalized hook lengths in symbols and partitions

Christine Bessenrodt, Jean-Baptiste Gramain, Jørn B. Olsson

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
7 Downloads (Pure)


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 languageEnglish
Pages (from-to)309-332
Number of pages24
JournalJournal of Algebraic Combinatorics
Issue number2
Early online date8 Dec 2011
Publication statusPublished - Sept 2012


  • symbols
  • hooks
  • hook lengths
  • partitions
  • core
  • quotient


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