Construct families of Mondrian partitions

Construct families of Mondrian partitions of n × n squares, clarifying how such families can be systematically generated beyond individual partitions produced by the strip-tiling construction.

Background

The paper develops a strip-tiling construction and an algorithm that produces individual Mondrian partitions with defect O(n^{5/6}). In the concluding remarks, the authors ask how to extend these constructions into families of partitions, potentially providing broader structural understanding or systematically generated examples.