### Abstract

We show that the way to partition a unit square into k^{2}+s rectangles, for s=1 or s=-1, so as to minimize the largest perimeter of the rectangles, is to have k-1 rows of k identical rectangles and one row of k+s identical rectangles, with all rectangles having the same perimeter. We also consider the analogous problem for partitioning a rectangle into n rectangles and describe some possible approaches to it.

Original language | English (US) |
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Pages (from-to) | 111-119 |

Number of pages | 9 |

Journal | Discrete Mathematics |

Volume | 103 |

Issue number | 2 |

DOIs | |

State | Published - May 27 1992 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Alon, N., & Kleitman, D. J. (1992). Partitioning a rectangle into small perimeter rectangles.

*Discrete Mathematics*,*103*(2), 111-119. https://doi.org/10.1016/0012-365X(92)90261-D