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On Minimal-Perimeter Lattice Animals

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12118))

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Abstract

A lattice animal is a connected set of cells on a lattice. The perimeter of a lattice animal A consists of all the cells that do not belong to A, but that have a least one neighboring cell of A. We consider minimal-perimeter lattice animals, that is, animals whose periemeter is minimal for all animals of the same area, and provide a set of conditions that are sufficient for a lattice to have the property that inflating all minimal-perimeter animals of a certain size yields (without repetitions) all minimal-perimeter animals of a new, larger size. We demonstrate this result for polyhexes (animals on the two-dimensional hexagonal lattice).

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Authors and Affiliations

  1. Department of Computer Science, The Technion—Israel Institute of Technology, 3200003, Haifa, Israel

    Gill Barequet & Gil Ben-Shachar

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  1. Gill Barequet
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  2. Gil Ben-Shachar
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Correspondence to Gill Barequet .

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Editors and Affiliations

  1. University of São Paulo, São Paulo, Brazil

    Yoshiharu Kohayakawa

  2. University of Campinas, Campinas, Brazil

    Flávio Keidi Miyazawa

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Barequet, G., Ben-Shachar, G. (2020). On Minimal-Perimeter Lattice Animals. In: Kohayakawa, Y., Miyazawa, F.K. (eds) LATIN 2020: Theoretical Informatics. LATIN 2021. Lecture Notes in Computer Science(), vol 12118. Springer, Cham. https://doi.org/10.1007/978-3-030-61792-9_41

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  • DOI: https://doi.org/10.1007/978-3-030-61792-9_41

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-61791-2

  • Online ISBN: 978-3-030-61792-9

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