Exhaustive generation of ‘Mrs. Perkins’s quilt’ square dissections for low orders

Dissections of a square into smaller squares, with the smaller squares having relatively prime sizes, are known as Mrs. Perkins’s quilts. A representation of these dissections using graphs is presented. The edges are directed and coloured North–South or West–East, and the graph corresponds naturally to the dissection. This representation allowed the exhaustive generation of all dissections up to order 18, using the plantri software. The results were cross-checked by generating all dissections of small sizes using a direct approach. The results confirm, extend and introduce several integer sequences.