Minimal Bar Tableaux

2003/11/24 by Peter Clifford, Clifford, Peter
Mathematics · #05E05 #05E10 #20C25 #20C30 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #math.CO #msc:05E05 #msc:05E10 #msc:20C25 #msc:20C30

paper · pdf · doi:10.48550/arxiv.math/0311418

12 pages, 7 figures

arxiv created 2003/11/24 · openalex publication_date 2003/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by Stanley's results in \citeSt02, we generalize the rank of a partition λ to the rank of a shifted partition S(λ). We show that the number of bars required in a minimal bar tableau of S(λ) is max(o, e + (ℓ(λ) mod 2)), where o and e are the number of odd and even rows of λ. As a consequence we show that the irreducible projective characters of S_n vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur's Q_λ symmetric functions in terms of the power sum symmetric functions.

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