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.
A combinatorial proof that Schubert vs. Schur coefficients are nonnegative
A combinatorial proof of a relationship between maximal $(2k-1,2k+1)$ and $(2k-1,2k,2k+1)$-cores
A combinatorial proof of the Rogers-Ramanujan and Schur identities
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