Enveloping Operads and Bicolored Noncrossing Configurations

Abstract

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

2000 AMS Subject Classification::

• 05E99

Keywords::

• operad
• colored operad
• tree
• noncrossing configuration

Notes

¹Available at http://www.research.att.com/njas/sequences/.

²Available at http://www.sagemath.org.

³See http://combinat.sagemath.org.