English

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