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2011 Challenging Computations of Hilbert Bases of Cones Associated with Algebraic Statistics
Winfried Bruns, Raymond Hemmecke, Bogdan Ichim, Matthias Köppe, Christof Söger
Experiment. Math. 20(1): 25-33 (2011).


In this paper we present two independent computational proofs that the monoid derived from 5 × 5 × 3 contingency tables is normal, completing the classification by Hibi and Ohsugi. We show that Vlach’s vector disproving normality for the monoid derived from 6 × 4 × 3 contingency tables is the unique minimal such vector up to symmetry. Finally, we compute the full Hilbert basis of the cone associated with the nonnormal monoid of the semigraphoid for |N| = 5. The computations are based on extensions of the packages LattE-4ti2 and Normaliz.


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Winfried Bruns. Raymond Hemmecke. Bogdan Ichim. Matthias Köppe. Christof Söger. "Challenging Computations of Hilbert Bases of Cones Associated with Algebraic Statistics." Experiment. Math. 20 (1) 25 - 33, 2011.


Published: 2011
First available in Project Euclid: 6 October 2011

zbMATH: 1273.13052
MathSciNet: MR2802722

Primary: 13P99 , 14M25 , 52B20

Keywords: Affine monoid , Contingency table , Hilbert basis , normalization , rational cone

Rights: Copyright © 2011 A K Peters, Ltd.


Vol.20 • No. 1 • 2011
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