%0 Journal Article %T Free dendriform dialgebras: reformulation and application in free probability. Part I %A Leroux Philippe %J Mathematics %D 2004 %I arXiv %X We propose a reformulation of some results known on the free dendriform dialgebra on one generator from a parenthesis point of view. This turns out to be more tractable and point out a connection to free probability by identifying noncrossing partitions with binary trees and by introducing the concept of NCP-operad. %U http://arxiv.org/abs/math/0408348v1