2021/07/12 by Guoce Xin, Xin, Guoce, Yingrui Zhang +3
Computer Science · Mathematics · Physics and Astronomy · #Graph Labeling and Dimension Problems #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications
paper · pdf · doi:10.48550/arxiv.2107.05259
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 5. 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.