Séminaire Lotharingien de Combinatoire, B72b (2014), 15 pp.

Patrick Dehornoy and Philippe Biane

Dual Garside Structure of Braids and Free Cumulants of Products

Abstract. We count the n-strand braids whose normal decomposition has length at most 2 in the dual braid monoid~Bn+* by reducing the question to a computation of free cumulants for a product of independent variables, for which we establish a general formula.

Received: July 17, 2014. Accepted: October 15, 2014. Final Version: November 10, 2014.

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