Coassociative magmatic bialgebras and the Fine numbers

Details Coassociative magmatic bialgebras and the Fine numbers Coassociative magmatic bialgebras and the Fine numbers

2006-09-05

arxiv.org/abs/math/0609125v1

J. Algebraic Combin. 28 (2008), no. 1, 97-114

Mathematics

Rings and Algebras

17 pages

Scientific paper

We prove a structure theorem for the connected coassociative magmatic bialgebras. The space of primitive elements is an algebra over an operad called the primitive operad. We prove that the primitive operad is magmatic generated by n-2 operations of arity n. The dimension of the space of all the n-ary operations of this primitive operad turns out to be the Fine number F_{n-1}. In short, the triple of operads (As, Mag, MagFine) is good.

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