# A Note on Split Rank of Intersection Cuts

In this note, we present a simple geometric argument to determine a lower bound on the split rank of intersection cuts. As a first step of this argument, a polyhedral subset of the lattice-free convex set that is used to generate the intersection cut is constructed. We call this subset the restricted lattice-free set. It is then shown that \$\lceil \textrm{log}_2 (l)\rceil\$ is a lower bound on the split rank of the intersection cut, where \$l\$ is the number of integer points lying on the boundary of the restricted lattice-free set satisfying the condition that no two points lie on the same facet of the restricted lattice-free set. The use of this result is illustrated to obtain a lower bound of \$\lceil \textrm{log}_2( n +1) \rceil\$ on the split rank of \$n\$-row mixing inequalities.

CORE DP 56, 2008