Challenging Computations of Hilbert Bases of Cones Associated with Algebraic Statistics

DOI10.1080/10586458.2011.544574zbMath1273.13052arXiv1001.4145OpenAlexW1967008640MaRDI QIDQ4915371

Christof Söger, Winfried Bruns, Raymond Hemmecke, Matthias Köppe, Bogdan Ichim

Publication date: 10 April 2013

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.4145

zbMATH Keywords

normalizationHilbert basiscontingency tableaffine monoidrational cone

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Parametrization (Chow and Hilbert schemes) (14C05) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25)

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Uses Software

• Normaliz
• 4ti2

Cites Work

• Normaliz: Algorithms for affine monoids and rational cones
• Toric geometry of cuts and splits
• Normality of cut polytopes of graphs is a minor closed property
• Conditions for the existence of solutions of the three-dimensional planar transportation problem
• Normal binary graph models