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

Authors :
Chen, William Y. C.
Dou, Donna Q. J.
Tang, Robert L.
Yang, Arthur L. B.
Publication Year :
2008

Abstract

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.<br />Comment: 25 pages, 7 figures

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.0805.2782
Document Type :
Working Paper