Enumeration of Domino Tilings of an Aztec Rectangle with boundary defects

TL;DR

This paper extends the enumeration of domino tilings in Aztec rectangles to include boundary defects on all sides, generalizing previous results that considered defects on only one side.

Contribution

It provides a new enumeration formula for domino tilings of Aztec rectangles with boundary defects on all sides, broadening the scope of prior work.

Findings

Derived a general enumeration formula for all boundary defects

Extended Helfgott and Gessel's results to multiple sides

Enhanced understanding of tiling configurations with boundary defects

Abstract

Helfgott and Gessel gave the number of domino tilings of an Aztec Rectangle with defects of size one on the boundary of one side. In this paper we extend this to the case of domino tilings of an Aztec Rectangle with defects on all boundary sides.