Abstract
The simplicial complexK(A) is defined to be the collection of simplices, and their proper subsimplices, representing maximal lattice free bodies of the form (x: Ax⩽b), withA a fixed generic (n + 1) ×n matrix. The topological space associated withK(A) is shown to be homeomorphic to ℝn, and the space obtained by identifying lattice translates of these simplices is homeorphic to then-torus.
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The first author was partially supported by Hungarian NSF grants 1907 and 1909, and also by U.S. NSF grant CCR-9111491. The research of the second author was supported by DMS9103608 and the third author by NSF grant SES9121936.
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Bárány, I., Howe, R. & Scarf, H.E. The complex of maximal lattice free simplices. Mathematical Programming 66, 273–281 (1994). https://doi.org/10.1007/BF01581150
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DOI: https://doi.org/10.1007/BF01581150