Relaxations of the matroid axioms I: Independence, Exchange and Circuits
Relaxations of the matroid axioms I: Independence, Exchange and Circuits
Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial complexes. The resulting classes retain some of the matroid properties and allow us …