An Izergin-Korepin-type identity for the 8VSOS model, with applications to alternating sign matrices

Details An Izergin-Korepin-type identity for the 8VSOS model, with applications to alternating sign matrices An Izergin-Korepin-type identity for the 8VSOS model, with applications to alternating sign matrices

2008-01-08

arxiv.org/abs/0801.1229v2

Adv. Appl. Math. 43 (2009), 137-155

Mathematics

Combinatorics

22 pages. Essential changes in Section 8, explaining relation to three-colour model

Scientific paper

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.

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