Covering a square by small perimeter rectangles

N. Alon; D. J. Kleitman

doi:10.1007/BF02187679

Covering a square by small perimeter rectangles

N. Alon, D. J. Kleitman

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We show that if the unit square is covered by n rectangles, then at least one must have perimeter at least 4(2 m+1)/(n+m(m+1)), where m is the largest integer whose square is at most n. This result is exact for n of the form m(m+1) (or m²).

Original language	English (US)
Pages (from-to)	1-7
Number of pages	7
Journal	Discrete & Computational Geometry
Volume	1
Issue number	1
DOIs	https://doi.org/10.1007/BF02187679
State	Published - Dec 1986
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/BF02187679

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title = "Covering a square by small perimeter rectangles",

abstract = "We show that if the unit square is covered by n rectangles, then at least one must have perimeter at least 4(2 m+1)/(n+m(m+1)), where m is the largest integer whose square is at most n. This result is exact for n of the form m(m+1) (or m2).",

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year = "1986",

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journal = "Discrete & Computational Geometry",

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AU - Alon, N.

AU - Kleitman, D. J.

PY - 1986/12

Y1 - 1986/12

N2 - We show that if the unit square is covered by n rectangles, then at least one must have perimeter at least 4(2 m+1)/(n+m(m+1)), where m is the largest integer whose square is at most n. This result is exact for n of the form m(m+1) (or m2).

AB - We show that if the unit square is covered by n rectangles, then at least one must have perimeter at least 4(2 m+1)/(n+m(m+1)), where m is the largest integer whose square is at most n. This result is exact for n of the form m(m+1) (or m2).

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U2 - 10.1007/BF02187679

DO - 10.1007/BF02187679

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JO - Discrete & Computational Geometry

JF - Discrete & Computational Geometry

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ER -

Covering a square by small perimeter rectangles

Abstract

All Science Journal Classification (ASJC) codes

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