Operads of decorated cliques I: construction and quotients

Samuele Giraudo (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

We introduce a functorial construction C which takes unitary magmas as input and produces operads. The obtained operads involve configurations of chords labeled by elements of , called-decorated cliques and generalizing usual configurations of chords. By considering combinatorial subfamilies of-decorated cliques defined, for instance, by limiting the maximal number of crossing diagonals or the maximal degree of the vertices, we obtain suboperads and quotients of C. This leads to a new hierarchy of operads containing, among others, operads on noncrossing configurations, Motzkin configurations, forests, dissections of polygons, and involutions. Besides, the construction C leads to alternative definitions of the operads of simple and double multi-tildes, and of the gravity operad.

Domaines: Combinatoire [math.CO]

Samuele Giraudo. Operads of decorated cliques I: construction and quotients. Séminaire Lotharigien de Combinatoire, 2021. ⟨hal-03668999⟩