Enveloping operads and bicoloured noncrossing configurations

Frédéric Chapoton, Samuele Giraudo

Published 2013-10-16, updated 2014-10-13Version 2

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.