Journal of Algebraic Combinatorics

, Volume 36, Issue 1, pp 67–102

Signed enumeration of ribbon tableaux: an approach through growth diagrams

Article

DOI: 10.1007/s10801-011-0324-2

Cite this article as:
Gouyou-Beauchamps, D. & Nadeau, P. J Algebr Comb (2012) 36: 67. doi:10.1007/s10801-011-0324-2

Abstract

We give an extension of the famous Schensted correspondence to the case of ribbon tableaux, where ribbons are allowed to be of different sizes. This is done by extending Fomin’s growth diagram approach of the classical correspondence, in particular by allowing signs in the enumeration. As an application, we give in particular a combinatorial proof, based on the Murnaghan–Nakayama rule, for the evaluation of the column sums of the character table of the symmetric group.

Keywords

Ribbon tableaux Growth diagrams Murnaghan–Nakayama rule Garsia–Milne involution principle RSK correspondence 

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Laboratoire de Recherche en InformatiqueUniversité Paris SudOrsayFrance
  2. 2.Fakultät für MathematikUniversität WienViennaAustria

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