Rhombus Tilings of a Hexagon with Two Triangles Missing on the Symmetry Axis

We compute the number of rhombus tilings of a hexagon with sides n, n, N, n, n, N, where two triangles on the symmetry axis touching in one vertex are removed. The case of the common vertex being the center of the hexagon solves a problem posed by Propp.Comment: 16 pages, AmS-LaTeX, uses TeXDra

Enumeration of tilings of diamonds and hexagons with defects

We show how to count tilings of Aztec diamonds and hexagons with defects using determinants. In several cases these determinants can be evaluated in closed form. In particular, we obtain solutions to problems 1, 2, and 10 in James Propp's list of problems on enumeration of matchings