2 citations · 6 across the 6 of their papers we have counts for
6 papers
The Tutte q-Polynomial
Guus Bollen, Henry Crapo, Relinde Jurrius
-Matroids are defined on complemented modular support lattices. Minors of length 2 are of four types as in a "classical" matroid. Tutte polynomials of matroids are calc…
An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota
Henry Crapo
We sketch the outlines of Gian Carlo Rota's interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre of 1844 and 1862, as adapted and explained by Giusep…
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,…