Coassociative magmatic bialgebras and the Fine numbers
Abstract
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 Fn-1. In short, the triple of operads (As, Mag, MagFine) is good.
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