Le module dendriforme sur le groupe cyclique

Frédéric Chapoton (1)

1 ICJ - Institut Camille Jordan

The structure of anticyclic operad on the Dendriform operad defines in particular a matrix of finite order acting on the vector space spanned by planar binary trees. We compute its characteristic polynomial and propose a (compatible) conjecture for the characteristic polynomial of the Coxeter transformation for the Tamari lattice, which is mostly a square root of this matrix.

Mots clés: operad; characteristic polynomial; symmetric function

Domaines: Algèbres quantiques [math.QA]

Frédéric Chapoton. Le module dendriforme sur le groupe cyclique. Annales de l'Institut Fourier, 2008, 58 (7), pp.2333-2350. ⟨hal-00141653⟩