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International Symposium on Fundamentals of Computation Theory

FCT 2015: Fundamentals of Computation Theory pp 41–52Cite as

On the Enumeration of Permutominoes

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9210))

Abstract

Although the exact counting and enumeration of polyominoes remain challenging open problems, several positive results were achieved for special classes of polyominoes. We give an algorithm for direct enumeration of permutominoes [13] by size, or, equivalently, for the enumeration of grid orthogonal polygons [23]. We show how the construction technique allows us to derive a simple characterization of the class of convex permutominoes, which has been extensively investigated [5]. The approach extends to other classes, such as the row convex and the directed convex permutominoes.

Partially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020.

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Notes

  1. 1.

    Demos at http://www.dcc.fc.up.pt/~apt/genpoly.

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Acknowledgments

This paper is an extended version of the work presented at the XV Spanish Meeting on Computational Geometry (EGC 2013). The author would like to thank anonymous reviewers for insightful comments.

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Authors and Affiliations

  1. DCC & CMUP, Faculdade de Ciências, Universidade do Porto, Porto, Portugal

    Ana Paula Tomás

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  1. Ana Paula Tomás
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Correspondence to Ana Paula Tomás .

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Editors and Affiliations

  1. Université Paris Diderot, Paris, France

    Adrian Kosowski

  2. Université Bordeaux 1, Talence, France

    Igor Walukiewicz

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Tomás, A.P. (2015). On the Enumeration of Permutominoes. In: Kosowski, A., Walukiewicz, I. (eds) Fundamentals of Computation Theory. FCT 2015. Lecture Notes in Computer Science(), vol 9210. Springer, Cham. https://doi.org/10.1007/978-3-319-22177-9_4

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  • DOI: https://doi.org/10.1007/978-3-319-22177-9_4

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