Parikh factor matrices for finite words of rectangular Hilbert space filling curve
About this article
Keywords:
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
Atanasiu A, Martin-Vide C & Mateescu A, “On the injectivity of the Parikh matrix mapping”, Fundam. Inform., Vol.46, (2001), pp.783-793.
de Luca A, “On the combinatorics of finite words”, Theoretical Computer Science, Vol.218, (1999), pp.13-39.
Samuel H, “On Generalized Parikh Matrices for finite and infinite words”, Int. J. Comp.Appln., Vol.68, (2013), pp.37-39.
Mateescu A, Salomaa A, Salomaa K & Yu S, “A sharpening of
the Parikh mapping”, RAIRO Theoret. Inform. Appl., Vol.35, (2001), pp.551–564.
View more references (5)
Seebold P, “Tag systems for the Hilbert curve”, Discrete Maths. & Theo. Comp. Sci., Vol.9, No.2, (2007), pp.213-226.
Seebold P, Kitaev S & Mansour T, “Generating the Peano curve and counting occurrences ofsome patterns”, J. of Automata, Languages and Combinatorics, Vol.9, (2004), pp.439-455.
Kitaev S, “The sigma-sequence and occurrences of some patterns, subsequences and sub words”, Australasian J. Combin., Vol.29, (2004), pp.187–200.
Kitaev S, Mansour T & Seebold P, “Counting ordered patterns in words generated by morphisms”, Electronic J. of comb. number theory, Vol.8, (2008).
Thiagarajan K, Navaneetham K & Jeya Bharathi S, “Rectangular Hilbert Space Filling Curve through 7-Power Free Infinite Word”, Indian Journal of Science and Technology, Vol.9, No.28, (2016).