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Operads of decorated cliques I: construction and quotients

Abstract : 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.
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Contributor : Samuele Giraudo Connect in order to contact the contributor
Submitted on : Wednesday, June 1, 2022 - 12:05:44 PM
Last modification on : Thursday, June 23, 2022 - 6:29:33 AM


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  • HAL Id : hal-03668999, version 1



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



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