On the Computation of Hilbert Bases and Extreme Rays of Cones

2002/03/12 by Raymond Hemmecke, Hemmecke, Raymond · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.CO

paper · pdf · doi:10.48550/arxiv.math/0203105

arxiv created 2002/03/12 · openalex publication_date 2002/03/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present a novel project-and-lift approach to compute the set of minimal generators of the semigroup (Λ∩\Rⁿ₊,+) for lattices Λ⊆\Zⁿ. This problem class includes the computation of Hilbert bases of cones \z:Az=0,z∈\Rⁿ₊\ for integer matrices A. A similar approach can be used to compute only the extreme rays of such cones. Finally, some combinatorial applications and computational experience are presented.

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