Improved Packings of $n(n − 1)$ Unit Squares in a Square

descriptionPublicationkeyboard_double_arrow_right Article 05 Nov 2021Publisher:The Electronic Journal of CombinatoricsJournal:The Electronic Journal of Combinatorics, volume 28 (eissn: 1077-8926,

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Authors: M. Z. Arslanov; S. A. Mustafin; Z. K. Shangitbayev;

doi: 10.37236/8586

Improved Packings of $n(n − 1)$ Unit Squares in a Square

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Abstract

Let $s(n)$ be the side of the smallest square into which we can pack $n$ unit squares. The purpose of this paper is to prove that $s(n^2-n)<n$ for all $n\geq 12$. Besides, we show that $s(18^2-17) < 18, s(17^2-16) < 17,$ and $s(16^2-15) < 16.$

Related Organizations

Institute of Information and Computational Technologies
Kazakhstan
Almaty Management University
Kazakhstan

Keywords

packings, square, Packing and covering in $2$ dimensions (aspects of discrete geometry), Combinatorial aspects of packing and covering, unit squares

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