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Z-Tilings of Polyominoes and Standard Basis

  • Olivier Bodini
  • Bertrand Nouvel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)

Abstract

In this paper, we prove that for every set E of polyominoes (for us, a polyomino is a finite union of unit squares of a square lattice), we have an algorithm which decides in polynomial time, for every polyomino P, whether P has or not a ℤ-tiling (signed tiling) by translated copies of elements of E. Moreover, if P is ℤ-tilable, we can build a ℤ-tiling of P. We use for this the theory of standard basis on ℤ[X 1,...,X n ]. In application, we algorithmically extend results of Conway and Lagarias on ℤ-tiling problems.

Keywords

Standard Basis Hexagonal Lattice Generalize Coloring Minimal Polynomial Zero Divisor 
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 2004

Authors and Affiliations

  • Olivier Bodini
    • 1
  • Bertrand Nouvel
    • 2
  1. 1.LIRMMMontpellier Cedex 5France
  2. 2.LIP UMR 5668 CNRS-INRIA-ENS Lyon-Univ. Lyon 1Lyon Cedex 07France

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