Operads of Decorated Cliques I: Construction and Quotients
Séminaire lotharingien de combinatoire, Tome 79 (2018-2023)
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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.
@article{SLC_2018-2023_79_a6,
author = {Samuele Giraudo},
title = {Operads of {Decorated} {Cliques} {I:} {Construction} and {Quotients}},
journal = {S\'eminaire lotharingien de combinatoire},
publisher = {mathdoc},
volume = {79},
year = {2018-2023},
url = {http://geodesic.mathdoc.fr/item/SLC_2018-2023_79_a6/}
}
Samuele Giraudo. Operads of Decorated Cliques I: Construction and Quotients. Séminaire lotharingien de combinatoire, Tome 79 (2018-2023). http://geodesic.mathdoc.fr/item/SLC_2018-2023_79_a6/