A set-operad of formal fractions and dendriform-like sub-operads
JOURNAL OF ALGEBRA(2016)
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.
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关键词
Algebraic combinatorics,Operads,Dendriform
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