Reverse Split Rank

TL;DR

This paper characterizes integral polyhedra in any dimension that have an infinite reverse split rank, revealing complex geometric properties related to their split ranks.

Contribution

It provides a geometric characterization of integral polyhedra with infinite reverse split rank in arbitrary dimensions.

Findings

Existence of polyhedra with infinite reverse split rank in R^3.

A geometric criterion for infinite reverse split rank in R^n.

Extension of known results to higher dimensions.

Abstract

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