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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