Selberg integrals, Askey-Wilson polynomials and lozenge tilings of a hexagon with a triangular hole
Artikel i vetenskaplig tidskrift, 2016

We obtain an explicit formula for a certain weighted enumeration of lozenge tilings of a hexagon with an arbitrary triangular hole. The complexity of our expression depends on the distance from the hole to the center of the hexagon. This proves and generalizes conjectures of Ciucu et al., who considered the case of plain enumeration when the triangle is located at or very near the center. Our proof uses Askey-Wilson polynomials as a tool to relate discrete and continuous Selberg-type integrals. © 2015 Elsevier Inc.

Tiling

Askey-Wilson polynomial

Selberg integral

Enumeration

Plane partition

Lattice path

Författare

Hjalmar Rosengren

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Journal of Combinatorial Theory - Series A

0097-3165 (ISSN)

Vol. 138 29-59

Ämneskategorier

Matematik

DOI

10.1016/j.jcta.2015.09.006