Discrete Mathematics
Theory of linear and integer programming
Theory of linear and integer programming
An Introduction to Empty Lattice Simplices
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
Inequalities from Two Rows of a Simplex Tableau
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Facets of Two-Dimensional Infinite Group Problems
Mathematics of Operations Research
On an Analysis of the Strength of Mixed-Integer Cutting Planes from Multiple Simplex Tableau Rows
SIAM Journal on Optimization
An Analysis of Mixed Integer Linear Sets Based on Lattice Point Free Convex Sets
Mathematics of Operations Research
Computing with multi-row gomory cuts
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Lifting integer variables in minimal inequalities corresponding to lattice-free triangles
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
On the facets of mixed integer programs with two integer variables and two constraints
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
On the relative strength of split, triangle and quadrilateral cuts
Mathematical Programming: Series A and B
On degenerate multi-row Gomory cuts
Operations Research Letters
Projecting Lattice Polytopes Without Interior Lattice Points
Mathematics of Operations Research
On some generalizations of the split closure
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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A convex set with nonempty interior is maximal lattice-free if it is inclusion maximal with respect to the property of not containing integer points in its interior. Maximal lattice-free convex sets are known to be polyhedra. The precision of a rational polyhedron P in Rd is the smallest natural number s such that sP is an integral polyhedron. In this paper we show that, up to affine mappings preserving Zd, the number of maximal lattice-free rational polyhedra of a given precision s is finite. Furthermore, we present the complete list of all maximal lattice-free integral polyhedra in dimension three. Our results are motivated by recent research on cutting plane theory in mixed-integer linear optimization.