Séminaire Lotharingien de Combinatoire, B79g (2020), 43 pp.

Samuele Giraudo

Operads of Decorated Cliques I: Construction and Quotients

Abstract. We introduce a functorial construction C which takes unitary magmas M as input and produces operads. The obtained operads involve configurations of chords labeled by elements of M, called M-decorated cliques and generalizing usual configurations of chords. By considering combinatorial subfamilies of M-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 CM. This leads to a new hierarchy of operads containing, among others, operads on noncrossing configurations, Motzkin configurations, forests, dissections of polygons, and involutions. Moreover, the construction C leads to alternative definitions of the operads of simple and double multi-tildes, and of the gravity operad.


Received: March 16, 2018. Revised: August 3, 2020. Accepted: August 10, 2020.

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