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Quadratic Gröbner bases for smooth 3×3 transportation polytopes

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Abstract

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.

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Author information

Correspondence to Andreas Paffenholz.

Additional information

Both authors were supported by Emmy Noether grant HA 4383/1 of the German Research Foundation (DFG).

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Haase, C., Paffenholz, A. Quadratic Gröbner bases for smooth 3×3 transportation polytopes. J Algebr Comb 30, 477 (2009). https://doi.org/10.1007/s10801-009-0173-4

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Keywords

  • Toric ideal
  • Gröbner basis
  • Quadratic triangulation
  • Transportation polytope