Mihai Ciucu
and Christian Krattenthaler
A nonautomatic (!) application of Gosper's algorithm evaluates
a determinant from tiling enumeration
(13 pages)
Abstract.
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 nonautomatic fashion.
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