Selberg integrals, Askey-Wilson polynomials and lozenge tilings of a hexagon with a triangular hole

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:138

Article

Rosengren, Hjalmar^1,2 

[1] Chalmers Univ Technol, Dept Math Sci, SE-41296 Gothenburg, Sweden

[2] Gothenburg Univ, SE-41296 Gothenburg, Sweden

关键词: Plane partition;    Tiling;    Lattice path;    Enumeration;    Askey-Wilson polynomial;    Selberg integral;   

DOI  :  10.1016/j.jcta.2015.09.006

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free