2 4 N ov 2 00 3 MINIMAL BAR TABLEAUX
نویسنده
چکیده
Motivated by Stanley's results in [7], 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.
منابع مشابه
N ov 2 00 3 BOTTOM SCHUR FUNCTIONS
We give a basis for the space spanned by the sumˆs λ of the lowest degree terms in the expansion of the Schur symmetric functions s λ in terms of the power sum symmetric functions p µ , where deg(p i) = 1. These lowest degree terms correspond to minimal border strip tableaux of λ. The dimension of the space spanned byˆs λ , where λ is a partition of n, is equal to the number of partitions of n ...
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