3,122 research outputs found
Selberg integrals, Askey-Wilson polynomials and lozenge tilings of a hexagon with a triangular hole
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.Comment: 29 pages; minor changes from v
New proofs of determinant evaluations related to plane partitions
We give a new proof of a determinant evaluation due to Andrews, which has
been used to enumerate cyclically symmetric and descending plane partitions. We
also prove some related results, including a q-analogue of Andrews's
determinant.Comment: 25 page
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