2010/09/24 by Alain Goupil, Goupil Alain, Alain, Goupil +3
Computer Science · Mathematics · Physics and Astronomy · #05A15 #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Topological and Geometric Data Analysis #math.CO #msc:05A15
paper · pdf · doi:10.48550/arxiv.1009.4859
15 pages
arxiv created 2010/09/24 · openalex publication_date 2010/09/24 · arxiv updated 2010/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a family of 3D combinatorial objects that we define as minimal 3D polyominoes inscribed in a rectanglar prism. These objects are connected sets of unitary cubic cells inscribed in a given rectangular prism and of minimal volume under this condition. They extend the concept of 2D polyominoes inscribed in a rectangle defined in a previous work. Using their geometric structure and elementary combinatorial arguments, we construct generating functions of minimal 3D polyominoes in the form of rational functions. We also obtain a number of exact formulas and recurrences for sub-families of these polyominoes.