Sur une opérade ternaire liée aux treillis de Tamari


We introduce an anticyclic operad V given by a ternary generator and a quadratic relation. We show that it admits a natural basis indexed by planar binary trees. We then relate this construction to the familly of Tamari lattices (Yn)n≥0 by defining an isomorphism between V(2n + 1) and the Grothendieck group of the category modYn. This isomorphism maps the… (More)