Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419719 | Advances in Applied Mathematics | 2011 | 55 Pages |
Abstract
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 Kuperbergʼs 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. We also conjecture an explicit formula for the free energy of the model.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Hjalmar Rosengren,