
TL;DR
This paper investigates conditions for perfectly packing an infinite sequence of squares with decreasing side lengths into a rectangle of minimal area, extending previous results to a broader range of parameters.
Contribution
It extends Chalcraft's perfect packing results to a larger range of the parameter t, specifically from 1/2 to 2/3, using an algorithmic approach.
Findings
Perfect packings exist for 1/2 < t ≤ 2/3.
Extended the known range of t for perfect packings.
Established perfect packings for all t in [log_3 2, 2/3].
Abstract
It is known that . Meir and Moser asked what is the smallest such that all the squares of sides of length , , , can be packed into a rectangle of area . A packing into a rectangle of the right area is called perfect packing. Chalcraft packed the squares of sides of length , , , and he found perfect packing for . We will show based on an algorithm by Chalcraft that there are perfect packings if . Moreover we show that there is a perfect packing for all in the range .
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Taxonomy
Topicsgraph theory and CDMA systems · Limits and Structures in Graph Theory · Optimization and Packing Problems
