Parikh factor matrices for finite words of rectangular Hilbert space filling curve

  • Authors

    • S Jeya Bharathi
    • K Thiagarajan
    • K Navaneetham

    Received date: May 28, 2018

    Accepted date: May 28, 2018

    Published date: May 29, 2018

    https://doi.org/10.14419/ijet.v7i2.31.13396
  • Ordered patterns, rises, descents, parikh matrix, factors, rectangular space filling curve.

  • Abstract

    Ordered Factor Patterns in a word over an ordered alphabet aredefined.  Also, Parikh StrictlyAscending FactorMatrix and Parikh StrictlyDescending Factor Matrix of a given word are introduced.  The relation of these matrices with Ordered Factor Patterns is discussed.  Moreover, the ParikhStrictly Ascending FactorMatrices and the Parikh Strictly Descending FactorMatricesfor finitewords of Rectangular Hilbert Space Filling Curve are determined. 

     

  • References

    1. [1] Atanasiu A, Martin-Vide C & Mateescu A, “On the injectivity of the Parikh matrix mappingâ€, Fundam. Inform., Vol.46, (2001), pp.783-793.

      [2] de Luca A, “On the combinatorics of finite wordsâ€, Theoretical Computer Science, Vol.218, (1999), pp.13-39.

      [3] Samuel H, “On Generalized Parikh Matrices for finite and infinite wordsâ€, Int. J. Comp.Appln., Vol.68, (2013), pp.37-39.

      [4] Mateescu A, Salomaa A, Salomaa K & Yu S, “A sharpening of
      the Parikh mappingâ€, RAIRO Theoret. Inform. Appl., Vol.35, (2001), pp.551–564.

      [5] Seebold P, “Tag systems for the Hilbert curveâ€, Discrete Maths. & Theo. Comp. Sci., Vol.9, No.2, (2007), pp.213-226.

      [6] Seebold P, Kitaev S & Mansour T, “Generating the Peano curve and counting occurrences ofsome patternsâ€, J. of Automata, Languages and Combinatorics, Vol.9, (2004), pp.439-455.

      [7] Kitaev S, “The sigma-sequence and occurrences of some patterns, subsequences and sub wordsâ€, Australasian J. Combin., Vol.29, (2004), pp.187–200.

      [8] Kitaev S, Mansour T & Seebold P, “Counting ordered patterns in words generated by morphismsâ€, Electronic J. of comb. number theory, Vol.8, (2008).

      [9] Thiagarajan K, Navaneetham K & Jeya Bharathi S, “Rectangular Hilbert Space Filling Curve through 7-Power Free Infinite Wordâ€, Indian Journal of Science and Technology, Vol.9, No.28, (2016).

  • Downloads

  • How to Cite

    Jeya Bharathi, S., Thiagarajan, K., & Navaneetham, K. (2018). Parikh factor matrices for finite words of rectangular Hilbert space filling curve. International Journal of Engineering and Technology, 7(2.31), 50-55. https://doi.org/10.14419/ijet.v7i2.31.13396

    Received date: May 28, 2018

    Accepted date: May 28, 2018

    Published date: May 29, 2018