Enumeration of parallelogram polycubes
Discrete Mathematics
2021-05-04 v1 Combinatorics
Abstract
In this paper, we enumerate parallelogram polycubes according to several parameters. After establishing a relation between Multiple Zeta Function and the Dirichlet generating function of parallelogram polyominoes, we generalize it to the case of parallelogram polycubes. We also give an explicit formula and an ordinary generating function of parallelogram polycubes according to the width, length and depth, by characterizing its projections. Then, these results are generalized to polyhypercubes.
Cite
@article{arxiv.2105.00971,
title = {Enumeration of parallelogram polycubes},
author = {Abderrahim Arabi and Hacène Belbachir and Jean-Philippe Dubernard},
journal= {arXiv preprint arXiv:2105.00971},
year = {2021}
}
Comments
15 pages, 8 figures