Quadratic Gröbner bases for smooth 3×3 transportation polytopes

Authors:
Christian Haase;Andreas Paffenholz
Affiliations:
Fachbereich Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany 14195;Fachbereich Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany 14195
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2009

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Abstract

The toric ideals of 3脳3 transportation polytopes $\mathsf{T}_{\mathbf{rc}}$ are quadratically generated. The only exception is the Birkhoff polytope B 3.If $\mathsf{T}_{\mathbf{rc}}$ is not a multiple of B 3, these ideals even have square-free quadratic initial ideals. This class contains all smooth 3脳3 transportation polytopes.