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arXiv · alg-geom/9709026

On the width of lattice-free simplices

Jean-Michel Kantor
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Abstract

Among integral polytopes (vertices with integral coordinates), lattice-free polytopes - intersecting the lattice ONLY at their vertices- are of particular interestin combinatorics and geometry of numbers. A natural question is to measure their "width" (with respect to the integral lattice).There were no known examples of lattice-free polytopes with width bigger than 2 .We prove the following Theorem : Given any positive number $α$ strictly inferior to $1/e$, for d large enough there exists a lattice-free simplex of dimension d and width superior to $αd$.

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Jean-Michel Kantor. 1997-09-24. On the width of lattice-free simplices. https://arxiv.org/abs/alg-geom/9709026

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