A set-operad of formal fractions and dendriform-like sub-operads
Combinatorics
2013-07-02 v1
Abstract
We introduce an operad of formal fractions, abstracted from the Mould operads and containing both the Dendriform and the Tridendriform operads. We consider the smallest set-operad contained in this operad and containing four specific elements of arity two, corresponding to the generators and the associative elements of the Dendriform and Tridendriform operads. We obtain a presentation of this operad (by binary generators and quadratic relations) and an explicit combinatorial description using a new kind of bi-colored trees. Similar results are also presented for related symmetric operads.
Keywords
Cite
@article{arxiv.1307.0092,
title = {A set-operad of formal fractions and dendriform-like sub-operads},
author = {Frédéric Chapoton and Florent Hivert and Jean-Christophe Novelli},
journal= {arXiv preprint arXiv:1307.0092},
year = {2013}
}
Comments
31 pages