Tiling a rectangle with the fewest squares

Details Tiling a rectangle with the fewest squares Tiling a rectangle with the fewest squares

1994-11-28

arxiv.org/abs/math/9411215v1

Mathematics

Combinatorics

Scientific paper

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 $C$.

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