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

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arxiv 2311.02385 v1 pith:IWASGLIU submitted 2023-11-04 math.CO

Natalia García-Colín , Dimitri Leemans , Mia Mü{ss}ig , Érika Roldán This is my paper · ORCID
classification math.CO
keywords mondrianpartitionperfectthererectanglerectanglessamesquare
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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 $n\leq 1000$. Using the same algorithm we have been able to establish that there is no perfect Mondrian partition of a $n \times m$ rectangle for $n,m \leq 400$.

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