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arXiv · 1307.0092

A set-operad of formal fractions and dendriform-like sub-operads

Frédéric Chapoton·Florent Hivert·Jean-Christophe Novelli
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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.

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Frédéric Chapoton, Florent Hivert, Jean-Christophe Novelli. 2013-06-29. A set-operad of formal fractions and dendriform-like sub-operads. https://arxiv.org/abs/1307.0092

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