A non-automatic (!) application of Gosper's algorithm evaluates a determinant from tiling enumeration

Mihai Ciucu; Christian Krattenthaler

paper

A non-automatic (!) application of Gosper's algorithm evaluates a determinant from tiling enumeration

arXiv:math/0011047

Abstract

We evaluate the determinant $det_{1 \leq i, j \leq n} ((x - i + 2 j x + y + j) - (x + i + 2 j x + y + j))$ , which gives the number of lozenge tilings of a hexagon with cut off corners. A particularly interesting feature of this evaluation is that it requires the proof of a certain hypergeometric identity which we accomplish by using Gosper's algorithm in a non-automatic fashion.

14 pages, AmS-TeX, uses TeXDraw; minor modifications