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

Hjalmar Rosengren (Institutionen för matematiska vetenskaper, matematik)
Journal of combinatorial theory. Series A (0097-3165). Vol. 138 (2016), p. 29-59.
[Artikel, refereegranskad vetenskaplig]

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.

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

Denna post skapades 2015-11-25. Senast ändrad 2016-04-05.
CPL Pubid: 226275


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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