Lozenge tilings of a halved hexagon with an array of triangles removed from the boundary, part II

Authors

Tri Lai, University of Nebraska- LincolnFollow

Date of this Version

12-21-2018

Citation

2018 Authors

Comments

the electronic journal of combinatorics 25(4) (2018), #P4.58

Abstract

Proctor's work on staircase plane partitions yields an exact enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi later ex- tended this tiling enumeration to a halved hexagon with a triangle cut o from the boundary. In his previous paper, the author proved a common generalization of Proctor's and Rohatgi's results by enumerating lozenge tilings of a halved hexagon in the case an array of an arbitrary number of triangles has been removed from a non-staircase side. In this paper we consider the other case when the array of tri- angles has been removed from the staircase side of the halved hexagon. Our result also implies an explicit formula for the number of tilings of a hexagon with an array of triangles removed perpendicularly to the symmetry axis.