Enumeration of Specific Classes of Polycubes

@article{Champarnaud2013EnumerationOS,
  title={Enumeration of Specific Classes of Polycubes},
  author={Jean-Marc Champarnaud and Quentin Cohen-Solal and J. Dubernard and H. Jeanne},
  journal={Electron. J. Comb.},
  year={2013},
  volume={20},
  pages={P26}
}
The aim of this paper is to gather several results concerning the enumeration of specific classes of polycubes. We first consider two classes of $3$-dimensional vertically-convex directed polycubes: the plateau polycubes and the parallelogram polycubes. An expression of the generating function is provided for the former class, as well as an asymptotic result for the number of polycubes of each class with respect to volume and width. We also consider three classes of $d$-dimensional polycubes… Expand
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