A non-automatic (!) application of Gosper's algorithm evaluates a determinant from tiling enumeration
Ciucu, Mihai · Krattenthaler, Christian
Combinatorics
Classical Analysis and ODEs
05A15 (Primary) 05A16 05A17 05A19 05B45 33C20 52C20 (Secondary)
Original · EN
We evaluate the determinant ₁≤ ᵢ,ⱼ≤ ₙ(x+y+jx-i+2j-x+y+jx+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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