The minimum length of an axis-aligned rectangular tiling of a flat torus
Combinatorics
2026-03-06 v1
Abstract
A flat torus is the quotient of the Euclidean plane over a lattice generated by a basis, and an axis-aligned rectangular tiling of a flat torus is a partition into finitely many rectangles whose sides are axis-aligned. We provide the minimum sum of the perimeter of rectangles for an axis-aligned rectangular tiling, and prove that it is attainable by either exactly one rectangle or exactly two rectangles.
Keywords
Cite
@article{arxiv.2603.04765,
title = {The minimum length of an axis-aligned rectangular tiling of a flat torus},
author = {Hau-Yi Lin and Wu-Hsiung Lin and Gerard Jennhwa Chang},
journal= {arXiv preprint arXiv:2603.04765},
year = {2026}
}