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

TL;DR

This paper presents a new proof for the enumeration of lozenge tilings of quartered hexagons, expanding on existing formulas using Kuo's graphical condensation method.

Contribution

It introduces a novel proof technique for the tiling enumeration, generalizing Proctor's theorem on plane partitions within a maximal staircase.

Findings

Provides a new proof for the tiling enumeration formula

Generalizes Proctor's theorem on plane partitions

Uses Kuo's graphical condensation method

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".