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Generating and counting triangular systems

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Abstract

Lunnon has defined a triangularp-mino as an edge-connected configuration ofp cells from the triangle plane grid with vertices of degree 6. A triangular system is a triangularp-mino without any holes. On the other hand we can say that a triangular system is a part of a triangular grid with vertices of degree 6, consisting of all edges and vertices of some closed broken lineC without intersections (a circuit in the triangle grid), and all edges and vertices in the interior ofC. It is obvious that any closed broken lineC without intersections uniquely determines a triangular system. In this paper a method of generating triangular systems is presented.

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References

  1. S. W. Golomb,Polyominoes, Charles Scribner's, New-York, 1965.

    Google Scholar 

  2. W. F. Lunnon,Counting polyominoes, in:Computers in Number Theory, Academic Press, London, 1971, 347–372.

    Google Scholar 

  3. W. F. Lunnon,Counting hexagonal and triangular polyominoes, Graph Theory and Computing, New-York-London 1972, 87–100.

  4. D. H. Redelmeier,Counting polyominoes: yet another attack, Discrete Mathematics, Vol. 36, Num. 2, September 1981, 191–204.

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  5. I. Stojmenović, R. Tošić and R. Doroslovački,An algorithm for generating and counting hexagonal systems, Proceedings of the 6th Yugoslav Seminar on Graph Theory and Lectures for Research Seminar, Dubrovnik 1985, Institute of Mathematics, University of Novi Sad, to appear.

  6. R. Tošić and R. Doroslovački,Characterization of hexagonal systems, Rev. of Res., Fac. of Sci., math. ser., Novi Sad, Vol. 14, Num. 2, 1984, 201–209.

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  7. R. Tošić, R. Doroslivački and I. Stojmenović,Generating and counting of square systems, preprint, 1985.

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Authors and Affiliations

  1. Faculty of Engineering, University of Novi Sad, Veljka Vlahovića 3, 21000, Novi Sad, Yugoslavia

    Rade Doroslovački

  2. Institute of Mathematics, University of Novi Sad, dr Ilije Djuričića 4, 21000, Novi Sad, Yugoslavia

    Ivan Stojmenović & Ratko Tošić

Authors
  1. Rade Doroslovački
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  2. Ivan Stojmenović
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  3. Ratko Tošić
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Doroslovački, R., Stojmenović, I. & Tošić, R. Generating and counting triangular systems. BIT 27, 18–24 (1987). https://doi.org/10.1007/BF01937351

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  • DOI: https://doi.org/10.1007/BF01937351

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