English

Plateau Polycubes and Lateral Area

Combinatorics 2018-11-15 v1

Abstract

In this paper, we enumerate two families of polycubes, the directed plateau polycubes and the plateau polycubes, with respect to the width and a new parameter, the Lateral Area. We give an explicit formula and the generating function for each of the two families of polycubes. Moreover, some asymptotic results about plateau polycubes are provided. We also establish results concerning the enumeration of column-convex polyominoes that are useful to get asymptotic results of polycubes.

Cite

@article{arxiv.1811.05707,
  title  = {Plateau Polycubes and Lateral Area},
  author = {Abderrahim Arabi and Hacène Belbachir and Jean-Philippe Dubernard},
  journal= {arXiv preprint arXiv:1811.05707},
  year   = {2018}
}

Comments

15 pages, 15 figures

R2 v1 2026-06-23T05:15:01.769Z