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Facet Connectedness of Arithmetic Discrete Hyperplanes with Non-Zero Shift

  • Eric DomenjoudEmail author
  • Bastien Laboureix
  • Laurent Vuillon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)

Abstract

We present a criterion for the arithmetic discrete hyperplane Open image in new window to be facet connected when \(\theta \) is the connecting thickness Open image in new window . We encode the shift \(\mu \) in a numeration system associated with the normal vector Open image in new window and we describe an incremental construction of the plane based on this encoding. We deduce a connectedness criterion and we show that when the Fully Subtractive algorithm applied to Open image in new window has a periodic behaviour, the encodings of shifts \(\mu \) for which the plane is connected may be recognised by a finite state automaton.

Keywords

Discrete hyperplane Connectedness Connecting thickness Fully subtractive algorithm Numeration system Finite state automaton 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Eric Domenjoud
    • 1
    Email author
  • Bastien Laboureix
    • 2
  • Laurent Vuillon
    • 3
  1. 1.Univ. de Lorraine, CNRS, LoriaNancyFrance
  2. 2.Ecole Normale Supérieure CachanCachanFrance
  3. 3.Univ. Savoie Mont Blanc, CNRS, LAMAChambéryFrance

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