Exhaustive generation of `Mrs Perkins's quilt' square dissections for low orders
Combinatorics
2014-06-24 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1308.5420,
title = {Exhaustive generation of `Mrs Perkins's quilt' square dissections for low orders},
author = {Ed Wynn},
journal= {arXiv preprint arXiv:1308.5420},
year = {2014}
}
Comments
Expanded and corrected version, June 2014