A method to construct all the paving matroids over a finite set

Abstract

We give a characterization of paving matroids through their sets of hyperplanes and an algorithm to construct all of them. We also give a simple proof of Rota’s basis conjecture for the case of sparse-paving matroids and for the case of paving matroids of rank rr on a set of cardinality n≤2rn≤2r, and a counterexample to Oxley’s characterization of paving matroids.