Séminaire Lotharingien de Combinatoire, B79h (2023), 47 pp.
Samuele Giraudo
Operads of Decorated Cliques II: Noncrossing Cliques
Abstract.
A complete study of an operad NCM of noncrossing configurations of chords
introduced in previous work of the author is performed. This operad is defined on the
linear span of all noncrossing M-cliques. These are noncrossing configurations of
chords with arcs labeled by a unitary magma M. The magmatic product of M
intervenes for the computation of the operadic composition of M-cliques. We show
that this operad is binary, quadratic, and Koszul by considering techniques coming from
rewrite systems on trees. We also compute a presentation for its Koszul dual. Finally,
we explain how NCM allows one to obtain alternative constructions of already known
operads like operads of formal fractions and the operad of bicolored noncrossing
configurations.
Received: March 16, 2018.
Revised: January 26, 2023; June 11, 2023.
Accepted: August 23, 2023.
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