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The height of minimal Hilbert bases

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Abstract

For an integral polyhedral cone C = pos{a1,…,am, a i ∈ ℤd, a subset \(\cal B\)(C) ⊂ C ∩ ℤd is called a minimal Hilbert basis of C iff (i) each element of C∩ℤd can be written as a non-negative integral combination of elements of \(\cal B\)(C) and (ii) \(\cal B\)(C) has minimal cardinality with respect to all subsets of C ∩ ℤd for which (i) holds. We give a tight bound for the so-called height of an element of the basis which improves on former results.

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  1. Konrad-Zuse-Zentrum für Informationstechnik (ZIB) Berlin, Takustraße 7, D-14195, Berlin-Dahlem, Germany

    Martin Henk & Robert Weismantel

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  1. Martin Henk
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  2. Robert Weismantel
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Correspondence to Martin Henk.

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Henk, M., Weismantel, R. The height of minimal Hilbert bases. Results. Math. 32, 298–303 (1997). https://doi.org/10.1007/BF03322141

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