Graph insertion operads
Combinatorics
2021-04-27 v2 Quantum Algebra
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 commutative operad and the commutative magmatic operad.
Keywords
Cite
@article{arxiv.2002.10926,
title = {Graph insertion operads},
author = {Jean-Christophe Aval and Samuele Giraudo and Théo Karaboghossian and Adrian Tanasa},
journal= {arXiv preprint arXiv:2002.10926},
year = {2021}
}
Comments
12 pages. Extended abstract of arXiv:1912.06563