Skip to main content
Log in

Algorithm and computer-program search for variants of polyomino packings in plane

  • Crystallographic Software
  • Published:
Crystallography Reports Aims and scope Submit manuscript

Abstract

An algorithm and a computer program that can be used in the search for all possible periodic packings of a specified set of polyominoes with a specified packing factor have been developed. The algorithm is based on the method of discrete modeling of molecular packings.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. S. Fedorov, Principles of the Theory of Figures (Izd-vo AN SSSR, Moscow, 1953) [in Russian].

    Google Scholar 

  2. N. V. Belov, Structure of Ionic Crystals and Metal Phases (Izd-vo AN SSSR, Moscow, 1947) [in Russian].

    Google Scholar 

  3. A. I. Kitaigorodsky, Molecular Crystals (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

  4. A. V. Maleev, V. G. Rau, K. A. Potekhin, et al., Dokl. Akad. Nauk SSSR, 315, 1382 (1990).

    Google Scholar 

  5. A. V. Maleev, Crystallogr. Rep. 40(3), 354 (1995).

    MathSciNet  ADS  Google Scholar 

  6. S. W. Golomb, Am. Math. Monthly. 61, 672 (1954).

    Google Scholar 

  7. S. W. Golomb, Polyominoes (Scribner, New York, 1965; Mir, Moscow, 1975).

    Google Scholar 

  8. M. Gardner, Mathematical Puzzles and Diversions (The University of Chicago Press, Chicago, IL, 1987; Mir, Moscow, 1999).

    Google Scholar 

  9. M. Gardner, Mathematical Games (Mir, Moscow, 1974) [in Russian].

    Google Scholar 

  10. M. Gardner, Time Travel and other Mathematical Bewilderments (W. H. Freeman, New York, 1988; Mir, Moscow, 1990).

    MATH  Google Scholar 

  11. A. V. Maleev, A. E. Lysov, and K. A. Potekhin, Crystallogr. Rep. 43(5), 721 (1998).

    ADS  Google Scholar 

  12. A. V. Maleev, Crystallogr. Rep. 46(1), 165 (2001).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. V. Maleev.

Additional information

Original Russian Text © A.V. Maleev, 2013, published in Kristallografiya, 2013, Vol. 58, No. 5, pp. 749–756.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maleev, A.V. Algorithm and computer-program search for variants of polyomino packings in plane. Crystallogr. Rep. 58, 760–767 (2013). https://doi.org/10.1134/S1063774513040135

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063774513040135

Keywords

Navigation