Séminaire Lotharingien de Combinatoire, 84B.66 (2020), 12 pp.
Jean-Christophe Aval, Samuele Giraudo,
Théo Karaboghossian and Adrian Tanasa
Graph Insertion Operads
Abstract.
Using the combinatorial species setting, we propose two new operad structures on
multigraphs and on pointed oriented multigraphs. The former can be considered as a canonical
operad on multigraphs, directly generalizing the Kontsevich-Willwacher operad, and has many
interesting suboperads. The latter is a natural extension of the pre-Lie operad in a sense
developed here and related to the multigraph operad. We study some of the finitely generated
suboperads of the multigraph operad and establish links between them and the comutative
operad and the commutative magmatic operad.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
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