The srank Conjecture on Schur's $Q$-Functions

Details The srank Conjecture on Schur's $Q$-Functions The srank Conjecture on Schur's $Q$-Functions

2008-05-19

arxiv.org/abs/0805.2782v1

Mathematics

Combinatorics

25 pages, 7 figures

Scientific paper

We show that the shifted rank, or srank, of any partition $\lambda$ with distinct parts equals the lowest degree of the terms appearing in the expansion of Schur's $Q_{\lambda}$ function in terms of power sum symmetric functions. This gives an affirmative answer to a conjecture of Clifford. As pointed out by Clifford, the notion of the srank can be naturally extended to a skew partition $\lambda/\mu$ as the minimum number of bars among the corresponding skew bar tableaux. While the srank conjecture is not valid for skew partitions, we give an algorithm to compute the srank.

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