49 citations · 52 across the 6 of their papers we have counts for
6 papers
Splicing Matroids
Joseph E. Bonin, William R. Schmitt
We introduce and study a natural variant of matroid amalgams. For matroids M(A) and N(B) such that M/(A-B)=N(B-A), we define a splice of M and N to be a matroid L on the union of A…
Primitive elements in the matroid-minor Hopf algebra
Henry Crapo, William Schmitt
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 contra…
A unique factorization theorem for matroids
Henry Crapo, William Schmitt
We study the combinatorial, algebraic and geometric properties of the free product operation on matroids. After giving cryptomorphic definitions of free product in terms of indepen…
The Free product of Matroids
Henry Crapo, William Schmitt
We introduce a noncommutative binary operation on matroids, called free product. We show that this operation respects matroid duality, and has the property that, given only the car…
A free subalgebra of the algebra of matroids
Henry Crapo, William Schmitt
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,…
Renormalization as a functor on bialgebras
Christian Brouder, William Schmitt
The Hopf algebra of renormalization in quantum field theory is described at a general level. The products of fields at a point are assumed to form a bialgebra B and renormalization…