A free subalgebra of the algebra of matroids

Authors:
Henry Crapo;William Schmitt
Affiliations:
CAMS/EHESS, Paris Cedex, France;Department of Mathematics, The George Washington University, Washington, DC
Venue:
European Journal of Combinatorics
Year:
2005

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Abstract

This paper is an initial inquiry into the structure of the Hopf algebra of matroids with restriction-contraction coproduct. Using a family of matroids introduced by Crapo in 1965, we show that the subalgebra generated by a single point and a single loop in the dual of this Hopf algebra is free.