Diophantine Approximations and Integer Points of Cones

The purpose of this note is to present a relation between directed best approximations of a rational vector and the elements of the minimal Hilbert basis of certain rational pointed cones. Furthermore, we show that for a special class of these cones the integer Carathéodory property holds true.

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Received May 6, 1998

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ID="*" Supported by a "Leibniz Preis" of the German Science Foundation (DFG) awarded to M. Grötschel.

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ID="†" Supported by a "Gerhard-Hess-Forschungsförderpreis" of the German Science Foundation (DFG).

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Henk, M., Weismantel, R. Diophantine Approximations and Integer Points of Cones. Combinatorica 22, 401–408 (2002). https://doi.org/10.1007/s004930200019

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  • AMS Subject Classification (2000) Classes:  52C07, 90C27