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A Tomographical Characterization of L-Convex Polyominoes

  • Giusi Castiglione
  • Andrea Frosini
  • Antonio Restivo
  • Simone Rinaldi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3429)

Abstract

Our main purpose is to characterize the class of L-convex polyominoes introduced in [3] by means of their horizontal and vertical projections. The achieved results allow an answer to one of the most relevant questions in tomography i.e. the uniqueness of discrete sets, with respect to their horizontal and vertical projections. In this paper, by giving a characterization of L-convex polyominoes, we investigate the connection between uniqueness property and unimodality of vectors of horizontal and vertical projections. In the last section we consider the continuum environment; we extend the definition of L-convex set, and we obtain some results analogous to those for the discrete case.

Keywords

Integer Vector Vertical Projection Discrete Tomography Continuum Counterpart Monotone Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Giusi Castiglione
    • 1
  • Andrea Frosini
    • 2
  • Antonio Restivo
    • 1
  • Simone Rinaldi
    • 2
  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di PalermoPalermoItaly
  2. 2.Dipartimento di Scienze Matematiche ed InformaticheUniversità di SienaSienaItaly

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