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

JOURNAL OF ALGEBRA

卷:465

Article

Chapoton, Frederic¹  Hivert, Florent²  Novelli, Jean-Christophe³ 

[1] Univ Lyon 1, Inst Camille Jordan, F-69622 Villeurbanne, France

[2] Univ Paris 11, Rech Informat Lab, F-91405 Orsay, France

[3] Univ Marne La Vallee, Inst Gaspard Monge, 5 Blvd Descartes, F-77454 Champs Sur Marne 2, Marne La Vallee, France

关键词: Algebraic combinatorics;    Operads;    Dendriform;   

DOI  :  10.1016/j.jalgebra.2016.07.001

来源: Elsevier

【 摘 要 】

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-coloured trees. Similar results are also presented for related symmetric operads. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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