On lattice points in polyhedral cross-sections |
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Authors: | Nickolay M Korneenko Nickolay N Metelskij |
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Institution: | (1) Institute of Mathematics, Byelarus Academy of Sciences, Surganova 11, CIS 220072 Minsk, Byelarus |
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Abstract: | (a) We prove that the convex hull of anyk
d
+1 points of ad-dimensional lattice containsk+1 collinear lattice points. (b) For a convex polyhedron we consider the numbers of its lattice points in consecutive parallel
lattice hyperplanes (levels). We prove that if a polyhedron spans no more than 2
d−1 levels, then this string of numbers may be arbitrary. On the other hand, we give an example of a string of 2
d−1+1 numbers to which no convex polyhedron corresponds inR
d
. |
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Keywords: | |
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