Polytopes of minimal null designs

Abstract

Null designs form a vector space and there are only finite numberof minimal null designs(up to scalar multiple), hence it isnatural to look at the convex polytopes of minimal null designs.For example, when t=0,, k=1, the convex polytope of minimalnull designs is the polytope of roots of type A_n. In thisarticle, we look at the convex polytopes of minimal null designsand find many general properties on the vertices, edges,dimension, and some structural properties that might help tounderstand the structure of polytopes for big n, t through thestructure of smaller n, t.