On the number of factorizations of a full cycle

Authors:
John Irving
Affiliations:
Department of Combinatorics & Optimization, University of Waterloo, Canada
Venue:
Journal of Combinatorial Theory Series A
Year:
2006

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Abstract

We give a new expression for the number of factorizations of a full cycle into an ordered product of permutations of specified cycle types. This is done through purely algebraic means, extending recent work of Biane. We deduce from our result a remarkable formula of Poulalhon and Schaeffer that was previously derived through an intricate combinatorial argument.