Mixed-integer sets from two rows of two adjacent simplex bases

In 2007 we studied a mixed-integer set arising from two rows of a
simplex tableau. We showed that facets of such a set can be obtained from
lattice point free triangles and quadrilaterals associated with either three or
four variables. In this paper we generalize our findings and show that, when
upper bounds on the non-basic variables are also considered, further classes
of facets arise that cannot be obtained from triangles and quadrilaterals.
Specifically, when exactly one upper bound on a non-basic variable is intro-
duced, stronger inequalities that can be derived from pentagons involving up
to six variables also appear.