ZIB PaperWeb

A counterexample to an integer analogue of Caratheodorys theorem

SC 98-28 Winfried Bruns, Joseph Gubeladze, Martin Henk, Alexander Martin, Robert Weismantel: A counterexample to an integer analogue of Caratheodorys theorem (Erschienen in: Journal für die Reine und Angewandte Mathematik 510, 1999, pp. 179-185)

Abstract: 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.
(only electronic version available)
Keywords: Integral pointed cones, Hilbert basis, integral Carath‚odory property
MSC: 90C10