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A counterexample to an integer analogue of Caratheodorys theorem

Please always quote using this URN: urn:nbn:de:0297-zib-3718
  • For $n\geq 6$ we provide a counterexample to the conjecture that every integral vector of a $n$-dimensional integral polyhedral pointed cone $C$ can be written as a nonnegative integral combination of at most $n$ elements of the Hilbert basis of $C$. In fact, we show that in general at least $\lfloor 7/6 \cdot n \rfloor$ elements of the Hilbert basis are needed.

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Metadaten
Author:Winfried Bruns, Joseph Gubeladze, Martin Henk, Alexander Martin, Robert Weismantel
Document Type:ZIB-Report
Tag:Hilbert basis; Integral pointed cones; integral Carathéodory property
MSC-Classification:90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C10 Integer programming
Date of first Publication:1998/11/02
Series (Serial Number):ZIB-Report (SC-98-28)
ZIB-Reportnumber:SC-98-28
Published in:Appeared in: Journal für die Reine und Angewandte Mathematik 510, 1999, pp. 179-185
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