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 result of Proctor on enumeration of plane partitions contained in a "maximal staircase".
Bibliographical noteFunding Information:
The author wants to thank Christian Krattenthaler for helpful comments, and Ranjan Rohatgi for useful discussion. This research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation (grant no. DMS-0931945 ).
- Graphical condensation
- Perfect matchings
- Plane partitions