Constructing combinatorial operads from monoids
Combinatorics
2012-08-07 v1
Abstract
We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operad obtained from the additive monoid. These involve various familiar combinatorial objects: parking functions, packed words, planar rooted trees, generalized Dyck paths, Schr\"oder trees, Motzkin paths, integer compositions, directed animals, etc. We also retrieve some known operads: the magmatic operad, the commutative associative operad, and the diassociative operad.
Keywords
Cite
@article{arxiv.1208.0920,
title = {Constructing combinatorial operads from monoids},
author = {Samuele Giraudo},
journal= {arXiv preprint arXiv:1208.0920},
year = {2012}
}
Comments
12 pages