We express the matroid polytope PM of a matroid M as a signed Minkowski sum of simplices, and obtain a formula for the volume of PM . This gives a combinatorial expression for the...
The aim of this paper is to initiate the study of alcoved polytopes, which are polytopes arising from affine Coxeter arrangements. This class of convex polytopes includes many clas...
Consider the moment curve in the real Euclidean space Rd defined parametrically by the map : R Rd , t (t) = (t, t2 , . . . , td ). The cyclic d-polytope Cd(t1, . . . , tn) is t...
Several polynomials are of use in various enumeration problems concerning objects in oriented matroids. Chief among these is the Radon catalog. We continue to study these, as well ...
Abstract. A sweep-plane algorithm of Lawrence for convex polytope computation is adapted to generate random tuples on simple polytopes. In our method an affine hyperplane is swept ...