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On the Number of Factorizations of a Full Cycle

John Irving
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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 work of Biane. We deduce from our result a formula of Poulalhon and Schaeffer that was previously derived through an intricate combinatorial argument.

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John Irving. 2005-10-17. On the Number of Factorizations of a Full Cycle. https://arxiv.org/abs/math/0510362

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