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Encoding Centered Polyominoes by Means of a Regular Language

  • Daniela Battaglino
  • Jean Marc Fedou
  • Andrea Frosini
  • Simone Rinaldi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)

Abstract

In [3] the authors proposed a classification of convex polyominoes based on the number of changes of direction in the paths connecting any two cells of a polyomino. More precisely, a convex polyomino is k-convex if every pair of its cells can be connected by a monotone path with at most k changes of direction. In 1-convex (also called L-convex) polyominoes, any two cells can be connected by a path with at most one change of direction.

References

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    Castiglione, G., Frosini, A., Munarini, E., Restivo, A., Rinaldi, S.: Combinatorial aspects of L-convex polyominoes. European J. Combin. 28, 1724–1741 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
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    Castiglione, G., Restivo, A.: Reconstruction of L-convex Polyominoes. Electron. Notes Discrete Math. 12 (2003)Google Scholar
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    Duchi, E., Rinaldi, S., Schaeffer, G.: The number of Z-convex polyominoes. Advances in Applied Math. 40, 54–72 (2008)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Daniela Battaglino
    • 1
  • Jean Marc Fedou
    • 2
  • Andrea Frosini
    • 3
  • Simone Rinaldi
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità di SienaSienaItaly
  2. 2.Departement d’InformatiqueUNSNiceFrance
  3. 3.Dipartimento di Sistemi e InformaticaUniversità di FirenzeFirenzeItaly

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