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.
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Bodini, O., Nouvel, B. (2004). Z-Tilings of Polyominoes and Standard Basis. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_11
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DOI: https://doi.org/10.1007/978-3-540-30503-3_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23942-0
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