A classical theorem of MacMahon states that the number of lozenge tilings of
any centrally symmetric hexagon drawn on the triangular lattice is given by a
beautifully simple product formula. In this paper we present a counterpart of
this formula, corresponding to the {\it exterior} of a concave hexagon obtained
by turning 120 degrees after drawing each side (MacMahon's hexagon is obtained
by turning 60 degrees after each step).Comment: 22 page

Ciucu, Mihai