Geodesic
Enumeration of specific classes of polycubes
Jean-Marc Champarnaud1 ; Quentin Cohen-Solal2 ; Jean-Philippe Dubernard3 ; Hadrien Jeanne1
1LITIS-Université de Rouen
2INSA Rouen
3LITIS- Université de Rouen
The electronic journal of combinatorics, Tome 20 (2013) no. 4
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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 $(d\geq 3)$ and we state asymptotic results for the number of polycubes of each class with respect to volume and width.
DOI : 10.37236/3549
Classification : 05A15, 05A16
Mots-clés : enumeration, polycubes

Jean-Marc Champarnaud  1   ; Quentin Cohen-Solal  2   ; Jean-Philippe Dubernard  3   ; Hadrien Jeanne  1

1 LITIS-Université de Rouen
2 INSA Rouen
3 LITIS- Université de Rouen 
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     author = {Jean-Marc Champarnaud and Quentin Cohen-Solal and Jean-Philippe Dubernard and Hadrien Jeanne},
     title = {Enumeration of specific classes of polycubes},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {4},
     doi = {10.37236/3549},
     zbl = {1295.05030},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3549/}
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Jean-Marc Champarnaud; Quentin Cohen-Solal; Jean-Philippe Dubernard; Hadrien Jeanne. Enumeration of specific classes of polycubes. The electronic journal of combinatorics, Tome 20 (2013) no. 4. doi: 10.37236/3549

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