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Symmetric functions and Macdonald’s result for top connexion coefficients in the symmetric group. (English) Zbl 0830.20021
Summary: Macdonald (unpublished) gave an indirect proof that the connexion coefficients for certain symmetric functions coincide with the connexion coefficients of the class algebra of the symmetric group. We give a direct proof of this result and demonstrate the use of these functions in a number of combinatorial questions associated with ordered factorisations of permutations into factors of specified cycle-type, including factorisations considered up to commutation in the symmetric group. Several related properties of the symmetric functions are given.

MSC:
20C30 Representations of finite symmetric groups
05E05 Symmetric functions and generalizations
20B30 Symmetric groups
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