On the Height of the Minimal Hilbert Basis | Zendy

Jiyong Liu | Zendy; L. E. Trotter | Zendy; Günter M. Ziegler | Zendy

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On the Height of the Minimal Hilbert Basis

Author(s) -

Jiyong Liu,

L. E. Trotter,

Günter M. Ziegler

Publication year - 1993

Publication title -

resultate der mathematik

Language(s) - English

Resource type - Journals

ISSN - 0378-6218

DOI - 10.1007/bf03322309

Subject(s) - polyhedron , basis (linear algebra) , mathematics , dimension (graph theory) , hull , convex hull , regular polygon , generator (circuit theory) , hilbert series and hilbert polynomial , pure mathematics , hilbert space , hilbert–poincaré series , combinatorics , mathematical analysis , geometry , physics , power (physics) , quantum mechanics , marine engineering , engineering

We present an elementary proof of a result due to Ewald and Wessels: in a pointed, polyhedral cone of dimension n ≥ 3 with integer-valued generators, any linearly independent generator representation for a minimal Hilbert basis element has coefficient sum less than n — 1. Our proof makes explicit use of the geometry of the polyhedron given by the convex hull of the Hilbert basis elements.

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