A free subalgebra of the algebra of matroids
  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. 
Henry Crapo (EHESS, Paris), William Schmitt (George Washington   University)