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

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

2000-11-08

arxiv.org/abs/math/0011047v2

Rocky Mountain J. Math. 32 (2002), 589-605.

Mathematics

Combinatorics

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

Scientific paper

We evaluate the determinant $\det_{1\leq i,j\leq n}(\binom{x+y+j}{x-i+2j}-\binom{x+y+j}{x+i+2j})$, 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.

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