Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometryVol. 40, No. 1, pp. 153-161 (1999)

On a Hadwiger-Wills Inequality Concerning Lattice Points

Krzysztof Kolodziejczyk

Institute of Mathematics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland, e-mail:

Abstract: There is an interesting inequality due to Hadwiger and Wills which shows that the difference between the number of lattice points in a given planar lattice polygon and the number of lattice points in its translate by an arbitrary vector whose coordinates are not both integers is always greater than or equal to the Euler characteristic of the polygon. In this note we give a few comments on the inequality when planar lattice polygons are replaced by higher dimensional integral polyhedra. Moreover we check the validity of the inequality in the case of planar $H$-polygons.

Classification (MSC91): 52B20, 52B11, 11H06

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