Dual Garside structure of braids and free cumulants of products
  We count the n-strand braids whose normal decomposition has length at most two 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. 
Philippe Biane (LIGM), Patrick Dehornoy (LMNO)
math.CO