A set-operad of formal fractions and dendriform-like sub-operads - Laboratoire Interdisciplinaire des Sciences du Numérique Access content directly
Journal Articles Journal of Algebra Year : 2016

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

Frédéric Chapoton
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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Dates and versions

hal-00839697 , version 1 (29-06-2013)

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Cite

Frédéric Chapoton, Florent Hivert, Jean-Christophe Novelli. A set-operad of formal fractions and dendriform-like sub-operads. Journal of Algebra, 2016, 465, pp.322-355. ⟨10.1016/j.jalgebra.2016.07.001⟩. ⟨hal-00839697⟩
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