Reverse Split Rank

Michele Conforti, Alberto Del Pia, Marco Di Summa, Yuri Faenza

Abstract: The reverse split rank of an integral polytope P is defined as the supremum of the split ranks of all rational polyhedra whose integer hull is P. Already in ℝ3 there exist polytopes with infinite reverse split rank. We give a geometric characterization of the integral polytopes in ℝ n with infinite reverse split rank.