The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, II
Abstract
We compute the number of rhombus tilings of a hexagon with side lengths N,M,N,N,M,N, with N and M having the same parity, which contain a particular rhombus next to the center of the hexagon. The special case N=M of one of our results solves a problem posed by Propp. In the proofs, Hankel determinants featuring Bernoulli numbers play an important role.
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