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A $q$-enumeration of lozenge tilings of a hexagon with four adjacent triangles removed from the boundary (1502.01679v5)
Published 5 Feb 2015 in math.CO
Abstract: MacMahon proved a simple product formula for the generating function of plane partitions fitting in a given box. The theorem implies a $q$-enumeration of lozenge tilings of a semi-regular hexagon on the triangular lattice. In this paper we generalize MacMahon's classical theorem by $q$-enumerating lozenge tilings of a new family of hexagons with four adjacent triangles removed from their boundary.