Dual Garside structure of braids and free cumulants of products

Philippe Biane (1) , Patrick Dehornoy (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Mots clés: braid group; dual braid monoid; Garside normal form; generating function; free cumulants; independent random variables; noncrossing partitions

Domaines: Combinatoire [math.CO]

Philippe Biane, Patrick Dehornoy. Dual Garside structure of braids and free cumulants of products. 2014. ⟨hal-01018936v2⟩