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Fully Leafed Tree-Like Polyominoes and Polycubes

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Combinatorial Algorithms (IWOCA 2017)

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Abstract

We present and prove recursive formulas giving the maximal number of leaves in tree-like polyominoes and polycubes of size n. We call these tree-like polyforms fully leafed. The proof relies on a combinatorial algorithm that enumerates rooted directed trees that we call abundant. We also show how to produce a family of fully leafed tree-like polyominoes and a family of fully leafed tree-like polycubes for each possible size, thus gaining insight into their geometric characteristics.

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Correspondence to Alexandre Blondin Massé .

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Blondin Massé, A., de Carufel, J., Goupil, A., Samson, M. (2018). Fully Leafed Tree-Like Polyominoes and Polycubes. In: Brankovic, L., Ryan, J., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2017. Lecture Notes in Computer Science(), vol 10765. Springer, Cham. https://doi.org/10.1007/978-3-319-78825-8_17

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  • DOI: https://doi.org/10.1007/978-3-319-78825-8_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78824-1

  • Online ISBN: 978-3-319-78825-8

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