The three-colour model with domain wall boundary conditions

Understand

We study the partition function for the three-colour model with domain wall boundary conditions.

• We express it in terms of certain special polynomials, which can be constructed recursively.
• Our method generalizes Kuperberg's proof of the alternating sign matrix theorem, replacing the six-vertex model used by Kuperberg with the eight-vertex-solid-on-solid model.
• As applications, we obtain some combinatorial results on three-colourings.