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

2016/10/20 by Lai, Tri
#05A15 #05B45 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.06284

Abstract

Proctor's work on staircase plane partitions yields an enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi recently extended this tiling enumeration to a halved hexagon with a triangle removed from the boundary. In this paper we prove a generalization of the results of Proctor and Rohatgi by enumerating lozenge tilings of a halved hexagon in which an array of adjacent triangles has been removed from the boundary.

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