PreprintCC BY 4.0arXiv
New Upper bounds on the Mondrian Art Problem
Abstract
We present a new upper bound on the defect of the Mondrian Art Problem. The Mondrian Art Problem asks for a partition of an n × n square with rectangles of distinct dimensions such that the difference (defect) between the largest and smallest rectangle areas is minimized. We prove that for any n × n square, there exists a partition with defect O(n5/6), improving upon the previously conjectured O (n/log n) upper bound. We also implement an algorithm that provides empirical evidence supporting our theoretical bound.
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BibTeX
@misc{garrison2026upper,
title = {{New Upper bounds on the Mondrian Art Problem}},
author = {Thomas Garrison and Chris Seiler and Aliaksei Semchankau},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01998},
eprint = {2609.01998},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01998},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - New Upper bounds on the Mondrian Art Problem
AU - Thomas Garrison
AU - Chris Seiler
AU - Aliaksei Semchankau
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.01998
UR - https://arxiv.org/abs/2609.01998
AB - We present a new upper bound on the defect of the Mondrian Art Problem. The Mondrian Art Problem asks for a partition of an n × n square with rectangles of distinct dimensions such that the difference (defect) between the largest and smallest rectangle areas is minimized. We prove that for any n × n square, there exists a partition with defect O(n^5/6), improving upon the previously conjectured O (n/log n) upper bound. We also implement an algorithm that provides empirical evidence supporting our theoretical bound.
ER -