2012/08/04 by Samuele Giraudo · 1 citation
Mathematics · #math.CO
published as Formal Power Series and Algebraic Combinatorics, 229--240, 2012 · 12 pages
arxiv created 2012/08/04 · arxiv updated 2012/08/07
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, Schröder 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.