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تسجيل مستخدم جديدMinimal Bar Tableaux
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Peter Clifford
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Motivated by Stanleys results in cite{St02}, we generalize the rank of a partition $lambda$ to the rank of a shifted partition $S(lambda)$. We show that the number of bars required in a minimal bar tableau of $S(lambda)$ is max$(o, e + (ell(lambda) mathrm{mod} 2))$, where $o$ and $e$ are the number of odd and even rows of $lambda$. 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 Schurs $Q_{lambda}$ symmetric functions in terms of the power sum symmetric functions.
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