Enumeration of rhombus tilings of a hexagon which contain a fixed rhombus on its symmetry axis

Mihai Ciucu, Markus Fulmek, Christian Krattenthaler

We compute the number of rhombus tilings of a hexagon with sides $N,M,N,N,M,N$, which contain a fixed rhombus on the symmetry axis. A special case solves a problem posed by Jim Pro…