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6 papers · 2 filters
A categorification for the chromatic polynomial
Laure Helme-Guizon, Yongwu Rong
For each graph we construct graded cohomology groups whose graded Euler characteristic is the chromatic polynomial of the graph. We show the cohomology groups satisfy a long exact…
Multi-Path Matroids
Joseph E. Bonin, Omer Gimenez
We introduce the minor-closed, dual-closed class of multi-path matroids. We give a polynomial-time algorithm for computing the Tutte polynomial of a multi-path matroid, we describe…
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,…
Lattice Path Matroids: Structural Properties
Joseph E. Bonin, Anna de Mier
This paper studies structural aspects of lattice path matroids, a class of transversal matroids that is closed under taking minors and duals. Among the basic topics treated are dir…