A triangular gap of size two in a sea of dimers on a $60^\circ$ angle

TL;DR

This paper investigates the interaction of a specific triangular gap with the corner of a 60-degree angle in a dimer model, revealing a correlation pattern akin to electrostatic interactions.

Contribution

It introduces a new analysis of gap-corner interactions in dimer packings, linking geometric configurations to electrostatic analogies.

Findings

Correlation governed by product of distances to five images

Reveals electrostatic-like behavior in dimer gap interactions

Extends previous work on gap correlations in lattice models

Abstract

We consider a triangular gap of side two in a $60^\circ$ angle on the triangular lattice whose sides are zig-zag lines. We study the interaction of the gap with the corner as the rest of the angle is completely filled with lozenges. We show that the resulting correlation is governed by the product of the distances between the gap and its five images in the sides of the angle. This provides a new aspect of the parallel between the correlation of gaps in dimer packings and electrostatics developed by the first author in previous work.