Square tilings with prescribed combinatorics (Q1310155)

The paper discusses tilings of rectangles by squares with prescribed combinatorics for the intersection pattern of the tiles. Let \(T\) be a triangulation of a quadrilateral \(Q\), and let \(V\) and \(E\) be its sets of vertices and edges, respectively. Then it is proved that there is an essentially unique tiling of a rectangle \(R\) by squares \(Z_ v\), one of each \(v \in V\), such that \(Z_ u \cap Z_ v \neq \varnothing\) if \(\{u,v\} \in E\), and such that the squares at the corners of \(R\) correspond to the corners of \(Q\). The author also describes an algorithm for computing the tiling from \(T\).