Geodesic
Dual Garside Structure of Braids and Free Cumulants of Products
Séminaire lotharingien de combinatoire, Tome 72 (2014-2015)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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. 

@article{SLC_2014-2015_72_a1,
     author = {Patrick Dehornoy and Philippe Biane},
     title = {Dual {Garside} {Structure} of {Braids} and {Free} {Cumulants} of {Products}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {72},
     year = {2014-2015},
     url = {http://geodesic.mathdoc.fr/item/SLC_2014-2015_72_a1/}
}
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Patrick Dehornoy; Philippe Biane. Dual Garside Structure of Braids and Free Cumulants of Products. Séminaire lotharingien de combinatoire, Tome 72 (2014-2015). http://geodesic.mathdoc.fr/item/SLC_2014-2015_72_a1/