Geodesic
Quadratic Gröbner bases for smooth $3\times 3$ transportation polytopes
Journal of Algebraic Combinatorics, Tome 30 (2009) no. 4, pp. 477-489.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The toric ideals of $3\times 3$ transportation polytopes $T _{ rc}$ mathsfT_mathbfrc are quadratically generated. The only exception is the Birkhoff polytope $B _{3}$. If $T _{ rc}$ mathsfT_mathbfrc is not a multiple of $B _{3}$, these ideals even have square-free quadratic initial ideals. This class contains all smooth $3\times 3$ transportation polytopes.
Keywords: keywords toric ideal, Gröbner basis, quadratic triangulation, transportation polytope 
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     author = {Haase, Christian and Paffenholz, Andreas},
     title = {Quadratic {Gr\"obner} bases for smooth $3\times 3$ transportation polytopes},
     journal = {Journal of Algebraic Combinatorics},
     pages = {477--489},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2009__30_4_a5/}
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Haase, Christian; Paffenholz, Andreas. Quadratic Gröbner bases for smooth $3\times 3$ transportation polytopes. Journal of Algebraic Combinatorics, Tome 30 (2009) no. 4, pp. 477-489. http://geodesic.mathdoc.fr/item/JAC_2009__30_4_a5/