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There is no perfect Mondrian partition for squares of side lengths less than 1001

2023/11/04 by García-Colín, Natalia, Leemans, Dimitri, Müßig, Mia +1
#52-08 #52C20 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.02385

Abstract

In mathematics, a dissection of a square (or rectangle) into non-congruent rectangles is a Mondrian partition. If all the rectangles have the same area, it is called a perfect Mondrian partition. In this paper, we present a computational result by which we can affirm that there is no perfect Mondrian partition of a length n square for n≤ 1000. Using the same algorithm we have been able to establish that there is no perfect Mondrian partition of a n × m rectangle for n,m ≤ 400.

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