Reverse split rank

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

Abstract: The reverse split rank of an integral polyhedron $$P$$ P is defined as the supremum of the split ranks of all rational polyhedra whose integer hull is $$P$$ P . Already in $$\mathbb {R}^3$$ R 3 there exist polyhedra with infinite reverse split rank. We give a geometric characterization of the integral polyhedra in $$\mathbb {R}^n$$ R n with infinite reverse split rank.