Enumerating Magic Distinct Labellings of the Cube
Combinatorics
2021-07-13 v1
Abstract
We find by applying MacMahon's partition analysis that all magic labellings of the cube are of eight types, each generated by six basis elements. A combinatorial proof of this fact is given. The number of magic labellings of the cube is thus reobtained as a polynomial in the magic sum of degree . Then we enumerate magic distinct labellings, the number of which turns out to be a quasi-polynomial of period 720720. We also find the group of symmetry can be used to significantly simplify the computation.
Keywords
Cite
@article{arxiv.2107.05259,
title = {Enumerating Magic Distinct Labellings of the Cube},
author = {Guoce Xin and Yingrui Zhang and Zihao Zhang},
journal= {arXiv preprint arXiv:2107.05259},
year = {2021}
}
Comments
13 pages, 3 figures