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Hole-Free Partially Directed Animals

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Developments in Language Theory (DLT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11647))

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Abstract

We consider the class of hole-free partially directed animals. This is the class of all polyominoes P such that every cell of P can be reached from any cell in the first column of P with a path (inside P) which makes only North, South and East steps, and such that there is not a finite region of empty unitary squares which is surrounded by cells belonging to P. We provide a generation algorithm that allows us to enumerate in constant amortized time using O(n) space.

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References

  1. Barcucci, E., Del Lungo, A., Pergola, E., Pinzani, R.: Directed animals, forests and permutations. Discrete Math. 204(1–3), 41–71 (1999)

    Article  MathSciNet  Google Scholar 

  2. Bousquet-Mélou, M.: A method for the enumeration of various classes of column-convex polygons. Discrete Math. 154(1–3), 1–25 (1996)

    Article  MathSciNet  Google Scholar 

  3. Brocchi, S., Castiglione, G., Massazza, P.: On the exhaustive generation of k-convex polyominoes. Theor. Comput. Sci. 664, 54–66 (2017)

    Article  MathSciNet  Google Scholar 

  4. 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). https://doi.org/10.1007/978-3-319-07148-0_6

    Chapter  Google Scholar 

  5. Castiglione, G., Restivo, A.: Reconstruction of L-convex polyominoes. Electron. Notes Discrete Math. 12, 290–301 (2003)

    Article  MathSciNet  Google Scholar 

  6. 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), 60 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Delest, M.-P., Viennot, G.: Algebraic languages and polyominoes enumeration. Theor. Comput. Sci. 34(1–2), 169–206 (1984)

    Article  MathSciNet  Google Scholar 

  8. Duchi, E., Rinaldi, S., Schaeffer, G.: The number of Z-convex polyominoes. Adv. Appl. Math. 40(1), 54–72 (2008)

    Article  MathSciNet  Google Scholar 

  9. Formenti, E., Massazza, P.: From tetris to polyominoes generation. Electron. Notes Discrete Math. 59, 79–98 (2017)

    Article  MathSciNet  Google Scholar 

  10. Formenti, E., Massazza, P.: On the generation of 2-polyominoes. In: Konstantinidis, S., Pighizzini, G. (eds.) DCFS 2018. LNCS, vol. 10952, pp. 101–113. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94631-3_9

    Chapter  Google Scholar 

  11. Golomb, S.W.: Checker boards and polyominoes. Am. Math. Mon. 61, 675–682 (1954)

    Article  MathSciNet  Google Scholar 

  12. Jensen, I.: Enumerations of lattice animals and trees. J. Stat. Phys. 102(3), 865–881 (2001). https://doi.org/10.1023/A:1004855020556

    Article  MathSciNet  MATH  Google Scholar 

  13. Jensen, I., Guttmann, A.J.: Statistics of lattice animals (polyominoes) and polygons. J. Phys. A: Math. Gen. 33(29), L257–L263 (2000)

    Article  MathSciNet  Google Scholar 

  14. 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). https://doi.org/10.1007/978-3-642-22321-1_30

    Chapter  Google Scholar 

  15. Massazza, P.: On the generation of L-convex polyominoes. In: Proceedings of GASCom12, Bordeaux, 25–27 June 2012

    Google Scholar 

  16. Massazza, P.: On the generation of convex polyominoes. Discrete Appl. Math. 183, 78–89 (2015)

    Article  MathSciNet  Google Scholar 

  17. Privman, V., Barma, M.: Radii of gyration of fully and partially directed lattice animals. Z. Phys. B: Condens. Matter 57(1), 59–63 (1984). https://doi.org/10.1007/BF01679926

    Article  Google Scholar 

  18. Redner, S., Yang, Z.R.: Size and shape of directed lattice animals. J. Phys. A: Math. Gen. 15(4), L177–L187 (1982)

    Article  MathSciNet  Google Scholar 

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Correspondence to Paolo Massazza .

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Massazza, P. (2019). Hole-Free Partially Directed Animals. In: Hofman, P., Skrzypczak, M. (eds) Developments in Language Theory. DLT 2019. Lecture Notes in Computer Science(), vol 11647. Springer, Cham. https://doi.org/10.1007/978-3-030-24886-4_16

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  • DOI: https://doi.org/10.1007/978-3-030-24886-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24885-7

  • Online ISBN: 978-3-030-24886-4

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