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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~*B*_{n}^{+*}
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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