The topological structure of maximal lattice free convex bodies: The general case
Given a generic m×n matrix A, the simplicial complex K.(A) is defined to be the collection of simplices representing maximal lattice point free convex bodies of the form x∶Ax≤b. The main result of this paper is that the topological space associated with K(A) is homeo-morphic with Rm−1.
KeywordsLattice Point Convex Body Simplicial Complex Ideal Point Convex Polyhedron
Unable to display preview. Download preview PDF.
- 1.I. Bárány, R. Howe, H. E. Scarf: The complex of maximal lattice-free simplices (1993), 3rd IPCO conference, and Math. Progr. 66 (1994), 273–281.Google Scholar
- 2.D. E. Bell: A theorem concerning the integer lattice, Studies in Applied Math 56 (1977), 187–188.Google Scholar
- 3.J-P. Doignon: Convexity in Cristallographic lattices, J. of Geometry 3 (1973), 77–85.Google Scholar
- 4.L. Lovász: Geometry of numbers and integer programming in mathematical programming: Recent developments and applications, M. Iri and K. Tanabe (eds.), Kluwer, 1989, 177–210.Google Scholar
- 5.H. E. Scarf: Production sets with indivisibilities. Part I. Generalities, Econometrica 49 (1981), 1–32.Google Scholar
- 6.P. White: Discrete activity analysis, Ph.D Thesis, Yale University, Department of Economics, 1983.Google Scholar