Free dendriform dialgebras: reformulation and application in free probability. Part I

Mathematics – Combinatorics

Scientific paper

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21 pages, 4 figures

Scientific paper

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.

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