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arXiv · 2104.12381

Operads of decorated cliques I: Construction and quotients

Samuele Giraudo
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Abstract

We introduce a functorial construction $\mathsf{C}$ which takes unitary magmas $\mathcal{M}$ as input and produces operads. The obtained operads involve configurations of chords labeled by elements of $\mathcal{M}$, called $\mathcal{M}$-decorated cliques and generalizing usual configurations of chords. By considering combinatorial subfamilies of $\mathcal{M}$-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 $\mathsf{C} \mathcal{M}$. 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 $\mathsf{C}$ leads to alternative definitions of the operads of simple and double multi-tildes, and of the gravity operad.

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Samuele Giraudo. 2021-04-26. Operads of decorated cliques I: Construction and quotients. https://arxiv.org/abs/2104.12381

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