Dr. Brigitte Servatius, Worcester Polytechnic Institute

Matroids, maps and Delta-matroids

Whitney examined the abstract properties of linear independence and defined matroids via several equivalent axiom systems almost 100 years ago. Matroids have since found many applications, for example in rigidity theory.

By replacing the set difference by the symmetric difference in Whitney's basis axiom for matroids, Bouchet defined Delta-matroids. He described Delta-matroids for maps on surfaces. Using Tutte's combinatorial definition of a map we define a Delta-matroid purely combinatorially and show that it is equivalent to Bouchet's topological definition.