A Generalization of Aztec Diamond Theorem, Part II

TL;DR

This paper presents a new proof for a generalized Aztec diamond theorem involving 4-vertex regions on the square lattice, utilizing Kuo graphical condensation to offer an alternative approach.

Contribution

It introduces a novel proof method using Kuo graphical condensation for a generalized Aztec diamond theorem, expanding the combinatorial understanding of tilings.

Findings

New proof of the generalized Aztec diamond theorem

Application of Kuo graphical condensation technique

Enhanced combinatorial insight into lattice tilings

Abstract

The author gave a proof of a generalization of the Aztec diamond theorem for a family of $4$-vertex regions on the square lattice with southwest-to-northeast diagonals drawn in (Electron. J. Combin., 2014) by using a bijection between tilings and non-intersecting lattice paths. In this paper, we use Kuo graphical condensation to give a new proof.