Chris Eur: Coxeter matroids.
Abstract
We take an inefficient but grounded route to Coxeter matroids as natural generalizations of ordinary matroids. We begin by reexamining ordinary matroids and their most immediate generalization---flag matroids. Through examples of these and their properties, particularly in the realizable cases, we will have smelled enough of what the general Coxeter matroid must be. We then finally define Coxeter matroids and their polytopes, and show that the classical theorem of GGMS generalizes naturally.