On the Generation of 2-Polyominoes

  • Enrico FormentiEmail author
  • Paolo Massazza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10952)


The class of 2-polyominoes contains all polyominoes P such that for any integer i, the first i columns of P consist of at most 2 polyominoes. We provide a decomposition that allows us to exploit suitable discrete dynamical systems to define an algorithm for generating all 2-polyominoes of area n in constant amortized time and space O(n).


  1. 1.
    Bousquet-Mélou, M.: A method for the enumeration of various classes of column-convex polygons. Discrete Math. 154(1–3), 1–25 (1996)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Brocchi, S., Castiglione, G., Massazza, P.: On the exhaustive generation of k-convex polyominoes. Theor. Comput. Sci. 664, 54–66 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Castiglione, G., Massazza, P.: An efficient algorithm for the generation of Z-convex polyominoes. In: Barneva, R.P., Brimkov, V.E., Šlapal, J. (eds.) IWCIA 2014. LNCS, vol. 8466, pp. 51–61. Springer, Cham (2014). Scholar
  4. 4.
    Castiglione, G., Restivo, A.: Reconstruction of L-convex polyominoes. Electron. Notes Discrete Math. 12, 290–301 (2003)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Del Lungo, A., Duchi, E., Frosini, A., Rinaldi, S.: On the generation and enumeration of some classes of convex polyominoes. Electron. J. Comb. 11(1) (2004)Google Scholar
  6. 6.
    Delest, M.P., Viennot, G.: Algebraic languages and polyominoes enumeration. Theor. Comput. Sci. 34(1–2), 169–206 (1984)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Formenti, E., Massazza, P.: From tetris to polyominoes generation. Electron. Notes Discrete Math. 59, 79–98 (2017)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Golomb, S.W.: Checker boards and polyominoes. Am. Math. Monthly 61, 675–682 (1954)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Jensen, I.: Enumerations of lattice animals and trees. J. Stat. Phys. 102(3), 865–881 (2001)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Jensen, I.: Counting polyominoes: a parallel implementation for cluster computing. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J.J., Zomaya, A.Y. (eds.) ICCS 2003. LNCS, vol. 2659, pp. 203–212. Springer, Heidelberg (2003). Scholar
  11. 11.
    Mantaci, R., Massazza, P.: On the exhaustive generation of plane partitions. Theor. Comput. Sci. 502, 153–164 (2013)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Mantaci, R., Massazza, P.: From linear partitions to parallelogram polyominoes. In: Mauri, G., Leporati, A. (eds.) DLT 2011. LNCS, vol. 6795, pp. 350–361. Springer, Heidelberg (2011). Scholar
  13. 13.
    Mantaci, R., Massazza, P., Yunès, J.B.: An efficient algorithm for generating symmetric ice piles. Theor. Comput. Sci. 629(C), 96–115 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Massazza, P.: On the generation of convex polyominoes. Discrete Appl. Math. 183, 78–89 (2015)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Privman, V., Barma, M.: Radii of gyration of fully and partially directed lattice animals. Z. Phys. B Condens. Matter 57(1), 59–63 (1984)CrossRefGoogle Scholar
  16. 16.
    Privman, V., Forgacs, G.: Exact solution of the partially directed compact lattice animal model. J. Phys. A Math. Gen. 20(8), L543 (1987)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Redner, S., Yang, Z.R.: Size and shape of directed lattice animals. J. Phys. A Math. Gen. 15(4), L177 (1982)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Université Côte d’Azur (UCA), CNRS, I3SNiceFrance
  2. 2.Department of Theoretical and Applied Sciences - Computer Science SectionUniversità degli Studi dell’InsubriaVareseItaly

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