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

par Garcia-Colin, Natalia;Leemans, Dimitri ;Müßig, Mia;Roldán, Érika
Référence Discrete applied mathematics, 359, page (400-406)
Publication Publié, 2024-12-01

Article révisé par les pairs

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Résumé :

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.