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

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 $n\le 1000$. Using the same algorithm we have been able to establish that there is no perfect Mondrian partition of a $n\times m$ rectangle for $n,m\le 400$.