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

Abstract

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.