Hypercubic Self-Tilings
Combinatorics
2019-10-15 v1
Abstract
In 1946 Fine and Niven posed problem E724, asking to demonstrate that every hypercube can be tiled by any number of hypercubic tiles larger than some value. This requires only basic number theory, but the problem of finding the smallest such number is much more involved. For the square this is known to be 5, and the cube 47. No other values are known. This paper improves the bound for tesseracts from 808 to 733.
Keywords
Cite
@article{arxiv.1910.06206,
title = {Hypercubic Self-Tilings},
author = {Benjamin Prather},
journal= {arXiv preprint arXiv:1910.06206},
year = {2019}
}