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A counterexample to an integer analogue of Carathéodory's theorem
- J. Reine Angew. Math
, 1998
"... For n>5 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 7n/6 elements of the ..."
Abstract
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Cited by 15 (6 self)
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For n>5 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 7n/6 elements of the Hilbert basis are needed.
