Annals of Combinatorics 9 (2005) 281-291

Minimal Bar Tableaux

Peter Clifford

Hamilton Institute, NUI Maynooth, Ireland

Received November 20, 2003

AMS Subject Classification: 05E05, 05E10, 20C25, 20C30

Abstract. Motivated by Stanley's results in [7], we generalize the rank of a partition to the rank of a shifted partition . We show that the number of bars required in a minimal bar tableau of is , where o and e are the number of odd and even rows of . As a consequence we show that the irreducible projective characters of Sn vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur's symmetric functions in terms of the power sum symmetric functions.

Keywords: bar tableau, strip tableau, rank, shifted partition, shifted shape, projective character, negative character, Schur Q-functions


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