On the Arithmetics of Discrete Figures

  • Alexandre Blondin Massé
  • Amadou Makhtar Tall
  • Hugo Tremblay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8370)


Discrete figures (or polyominoes) are fundamental objects in combinatorics and discrete geometry, having been studied in many contexts, ranging from game theory to tiling problems. In 2008, Provençal introduced the concept of prime and composed polyominoes, which arises naturally from a composition operator acting on these discrete figures. Our goal is to study further polyomino composition and, in particular, factorization of polyominoes as a product of prime ones. We provide a polynomial time (with respect to the perimeter of the polyomino) algorithm that allows one to compute such a factorization. As a consequence, primality of polyominoes can be decided in polynomial time.


Discrete figures polyominoes boundary words primality tiling morphism 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Alexandre Blondin Massé
    • 1
    • 2
  • Amadou Makhtar Tall
    • 1
  • Hugo Tremblay
    • 1
    • 2
  1. 1.Laboratoire d’informatique formelleUniversité du Québec à ChicoutimiChicoutimiCanada
  2. 2.Laboratoire de combinatoire et d’informatique mathématiqueUniversité du Québec à MontréalMontralCanada

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