Split rank of triange and quadrilateral inequalities

A simple relaxation consisting of two rows of a simplex tableau is a mixed-integer set with two equations, two free integer variables, and nonnegative continuous variables. Recently, Andersen et al. and Cornuéjols and Margot showed that the facet- defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. From an example given by Cook, Kannan and Schrijver it is known that one particular class of facet-defining triangle inequality does not have finite split rank. In this talk we show that all other facet-defining triangle and quadrilateral inequalities have finite split rank.