Séminaire Lotharingien de Combinatoire, 78B.15 (2017), 12 pp.
Combalgebraic Structures on Decorated Cliques
A new hierarchy of combinatorial operads is introduced, involving
families of regular polygons with configurations of arcs, called
decorated cliques. This hierarchy contains, among others, operads on
noncrossing configurations, Motzkin objects, forests, dissections of
polygons, and involutions. All this is a consequence of the definition
of a general functorial construction from unitary magmas to
operads. We study some of its main properties and show that this
construction includes the operad of bicolored noncrossing
configurations and the operads of simple and double multi-tildes. We
focus in more details on a suboperad of noncrossing decorated cliques
by computing its presentation, its Koszul dual, and showing that it is
a Koszul operad.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
The following versions are available: