Signed enumeration of ribbon tableaux

2009/11/17 by Dominique Gouyou-Beauchamps, Gouyou-Beauchamps, Dominique, Philippe Nadeau +1
Mathematics · #05A15 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #O5E10 #Random Matrices and Applications #math.CO #msc:05A15 #msc:O5E10

paper · pdf · doi:10.48550/arxiv.0911.3381

31 pages, 20 figures

arxiv created 2009/11/17 · openalex publication_date 2009/11/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an extension of the classical 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 between permutations and pairs of standard tableaux of the same shape, in particular by allowing signs in the enumeration. As an application we give a combinatorial proof for the column sums of the character table of the symmetric group.

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