The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, II

Details The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, II The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, II

1999-09-07

arxiv.org/abs/math/9909038v1

Europ. J. Combin. 21 (2000), 601-640.

Mathematics

Combinatorics

42 pages, AmS-LaTeX, uses TeXDraw

Scientific paper

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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