A differential operator for symmetric functions and the combinatorics of multiplying transpositions

Goulden, I. P.

doi:10.1090/S0002-9947-1994-1249468-3

A differential operator for symmetric functions and the combinatorics of multiplying transpositions
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Trans. Amer. Math. Soc. 344 (1994), 421-440 Request permission

Abstract:

By means of irreducible characters for the symmetric group, formulas have previously been given for the number of ways of writing permutations in a given conjugacy class as products of transpositions. These formulas are alternating sums of binomial coefficients and powers of integers. Combinatorial proofs are obtained in this paper by analyzing the action of a partial differential operator for symmetric functions.

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