Tiling a rectangle with the fewest squares

Richard Kenyon

Tiling a rectangle with the fewest squares

Combinatorics 2016-09-06 v1 Metric Geometry

Authors: Richard Kenyon

Abstract

We show that a square-tiling of a $p\times q$ rectangle, where $p$ and $q$ are relatively prime integers, has at least $\log_2p$ squares. If $q>p$ we construct a square-tiling with less than $q/p+C\log p$ squares of integer size, for some universal constant $C$ .

Keywords

tilings linear sets

Cite

@article{arxiv.math/9411215,
  title  = {Tiling a rectangle with the fewest squares},
  author = {Richard Kenyon},
  journal= {arXiv preprint arXiv:math/9411215},
  year   = {2016}
}