2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72282We 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.21 pages, 4 figuresCombinatoricsQuantum Algebra05C05; 06A07; 11A99; 46L54text