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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79071We 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.42 pages, AmS-LaTeX, uses TeXDrawCombinatorics05A15 05A16 05A17 05A19 05B45 11B68 30B70 33C20 33C45 52C20The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, IItext