A new proof for the number of lozenge tilings of quartered hexagons

Abstract: It has been proven that the lozenge tilings of a quartered hexagon on the triangular lattice are enumerated by a simple product formula. In this paper we give a new proof for the tiling formula by using Kuo's graphical condensation. Our result generalizes a Proctor's theorem on enumeration of plane partitions contained in a "maximal staircase".