Abstract :
[en] A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two
equations with two free integer variables and non-negative 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. Through a result by Cook et al., it is known that one particular class of facet-
defining triangle inequality does not have a finite split rank. In this paper, we show that all other
facet-defining triangle and quadrilateral inequalities have finite split rank. The proof is
constructive and given a facet-defining triangle or quadrilateral inequality we present an explicit
sequence of split inequalities that can be used to generate it.
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