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Jucys-Murphy Elements and a Combinatorial Proof of an Identity of S. Kerov (1004.4571v1)
Published 26 Apr 2010 in math.CO and math.RT
Abstract: Consider the elements of the group algebra CS_{n} given by R_{j}=Sigma_{i=1}{j-1}(ij), for 2<=j<=n. Jucys [3 - 5] and Murphy[7] showed that these elements act diagonally on elements of S_{n} and gave explicit formulas for the diagonal entries. As requested by the late S. Kerov, we give a combinatorial proof of this work in case j=n and present several similar results which arise from these combinatorial methods.
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