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

TL;DR

This paper generalizes previous results on lozenge tilings of halved hexagons by enumerating tilings with an array of boundary triangles removed, extending the combinatorial understanding of these tilings.

Contribution

It introduces a new enumeration formula for lozenge tilings of a halved hexagon with multiple boundary triangles removed, broadening prior specific cases.

Findings

Derived a general enumeration formula for complex boundary modifications

Extended previous tiling enumeration results to more general boundary conditions

Confirmed the enumeration through combinatorial proofs

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.