Geodesic
Primitive elements in the matroid-minor Hopf algebra
Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 43-64.

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

Summary: We introduce the $matroid-minor$ coalgebra $C$, which has labeled matroids as distinguished basis and coproduct given by splitting a matroid into a submatroid and complementary contraction in all possible ways. We introduce two new bases for $C$; the first of these is related to the distinguished basis by Möbius inversion over the rank-preserving weak order on matroids, the second by Möbius inversion over the suborder excluding matroids that are irreducible with respect to the free product operation. We show that the subset of each of these bases corresponding to the set of irreducible matroids is a basis for the subspace of primitive elements of $C$. Projecting $C$ onto the matroid-minor Hopf algebra $H$, we obtain bases for the subspace of primitive elements of $H$.
Classification : 05B35, 16W30, 05A15
Keywords: keywords matroid, free product, Hopf algebra, primitive elements 
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Crapo, Henry; Schmitt, William. Primitive elements in the matroid-minor Hopf algebra. Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 43-64. http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a8/