An Izergin-Korepin-type identity for the 8VSOS model, with applications to alternating sign matrices
Combinatorics
2014-06-16 v2 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We obtain a new expression for the partition function of the 8VSOS model with domain wall boundary conditions, which we consider to be the natural extension of the Izergin-Korepin formula for the six-vertex model. As applications, we find dynamical (in the sense of the dynamical Yang-Baxter equation) generalizations of the enumeration and 2-enumeration of alternating sign matrices. The dynamical enumeration has a nice interpretation in terms of three-colourings of the square lattice.
Keywords
Cite
@article{arxiv.0801.1229,
title = {An Izergin-Korepin-type identity for the 8VSOS model, with applications to alternating sign matrices},
author = {Hjalmar Rosengren},
journal= {arXiv preprint arXiv:0801.1229},
year = {2014}
}
Comments
22 pages. Essential changes in Section 8, explaining relation to three-colour model