Minimal Bar Tableaux |
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Authors: | Peter Clifford |
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Institution: | (1) CNRI, Dublin Institute of Technology, FOCAS Building DIT, Camden Row, Dublin 8, Ireland |
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Abstract: | Motivated by recent results of Stanley, 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 Sn vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur’s
Qλ symmetric functions in terms of the power sum symmetric functions.
Received November 20, 2003 |
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Keywords: | 05E05 05E10 20C25 20C30 |
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