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. © 2004 Published by Elsevier Ltd.
Crapo, H., & Schmitt, W. (2005). A free subalgebra of the algebra of matroids. European Journal of Combinatorics, 26(7), 1066–1085. https://doi.org/10.1016/j.ejc.2004.05.006