Enveloping operads and bicoloured noncrossing configurations

Frédéric Chapoton (1) , Giraudo Samuele (2)

1 ICJ - Institut Camille Jordan
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

An operad structure on certain bicoloured noncrossing configurations in regular polygons is studied. Motivated by this study, a general functorial construction of enveloping operad, with input a coloured operad and output an operad, is presented. The operad of noncrossing configurations is shown to be the enveloping operad of a coloured operad of bubbles. Several suboperads are also investigated, and described by generators and relations.

Mots clés: Noncrossing configuration; Operad; Coloured operad; Tree; Noncrossing configuration.

Domaines: Combinatoire [math.CO]; Algèbres quantiques [math.QA]

Frédéric Chapoton, Giraudo Samuele. Enveloping operads and bicoloured noncrossing configurations. Experimental Mathematics, 2014, 23 (Issue 3), pp.332--349. ⟨hal-00874014⟩