Enumeration of plateau polycubes with respect to their lateral area

Abderrahim Arabi (), Hacène Belbachir () and Jean-Philippe Dubernard ()
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Abderrahim Arabi: USTHB
Hacène Belbachir: USTHB
Jean-Philippe Dubernard: USTHB

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 538-554

Abstract: 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.

Keywords: Polycubes; Polyominoes; Enumeration; Generating function; Area; 05A15; 05B50. (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00385-3

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