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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