Quadratic Gröbner bases for smooth 3×3 transportation polytopes

  • Christian Haase
  • Andreas PaffenholzEmail author


The toric ideals of 3×3 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 3×3 transportation polytopes.


Toric ideal Gröbner basis Quadratic triangulation Transportation polytope 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Fachbereich Mathematik und InformatikFreie Universität BerlinBerlinGermany

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