Constructing combinatorial operads from monoids

Samuele Giraudo (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

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.

Domaines: Combinatoire [math.CO]

Samuele Giraudo. Constructing combinatorial operads from monoids. 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), 2012, Nagoya, Japan. pp.229--240, ⟨10.46298/dmtcs.3034⟩. ⟨hal-00790743⟩