Geodesic
Coassociative magmatic bialgebras and the Fine numbers.
Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 97-114.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Keywords: keywords bialgebra, generalized bialgebra, Hopf algebra, cartier-Milnor-Moore, Poincaré-Birkhoff-Witt, magmatic, operad, fine number, pre-Lie algebra 
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     title = {Coassociative magmatic bialgebras and the {Fine} numbers.},
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Holtkamp, Ralf; Loday, Jean-Louis; Ronco, María. Coassociative magmatic bialgebras and the Fine numbers.. Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 97-114. http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a6/