Square ice, alternating sign matrices and orthogonal polynomials
Filippo Colomo


Abstract
The six-vertex model (or square ice) with Domain Wall Boundary Conditions is of particular interest for its connections with various interesting combinatorial problems (plane partitions, domino tilings, alternating sign matrices (ASM)). Using standard techniques from the theory of orthogonal polynomials, we obtain in a simple and unified way exact results for the partition function and boundary correlators of the model, at particular values of parameters. This method, besides providing very simple alternative proofs to several results concerning ASM, allows to solve the long lasting problem of ASM refined 3-enumeration.

---

Elenco dei partecipanti al convegno di Bari.

---