English

A stability theorem on cube tessellations

Combinatorics 2018-07-16 v1

Abstract

It is shown that if a dd-dimensional cube is decomposed into n cubes, the side lengths of which belong to the interval (11n1/d+1,1],then\left(1-\frac{1}{n^{1/d}+1}, 1\right], then nisaperfect is a perfect d$-th power and all cubes are of the same size. This result is essentially tight.

Keywords

Cite

@article{arxiv.1807.05055,
  title  = {A stability theorem on cube tessellations},
  author = {Peter Frankl and Janos Pach},
  journal= {arXiv preprint arXiv:1807.05055},
  year   = {2018}
}

Comments

4 pages

R2 v1 2026-06-23T03:00:21.619Z