Challenging Computations of Hilbert Bases of Cones Associated with Algebraic Statistics
Autor(en): | Bruns, Winfried Hemmecke, Raymond Ichim, Bogdan Koeppe, Matthias Soeger, Christof |
Stichwörter: | Affine monoid; contingency table; Hilbert basis; Mathematics; normalization; rational cone | Erscheinungsdatum: | 2011 | Herausgeber: | TAYLOR & FRANCIS INC | Journal: | EXPERIMENTAL MATHEMATICS | Volumen: | 20 | Ausgabe: | 1 | Startseite: | 25 | Seitenende: | 33 | Zusammenfassung: | In this paper we present two independent computational proofs that the monoid derived from 5 x 5 x 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 x 4 x 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. |
ISSN: | 10586458 | DOI: | 10.1080/10586458.2011.544574 |
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