Precedence Matrices and words over some ordered alphabet

R. Stella Maragatham; V. Nithya Vani

doi:https://doi.org/10.14445/22315373/IJMTT-V52P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 52 | Number 1 | Year 2017 | Article Id. IJMTT-V52P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P506

Precedence Matrices and words over some ordered alphabet

R. Stella Maragatham, V. Nithya Vani

Citation :

R. Stella Maragatham, V. Nithya Vani, "Precedence Matrices and words over some ordered alphabet," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 1, pp. 40-47, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P506

Abstract

A word, mathematically expressed, is a sequence of symbols in a finite set, called an alphabet. Parikh matrix is an ingenious tool providing information on certain subsequences of a word, referred to as subwords. On the other hand, based on subwords of a word, the notion of Precedence matrix or p-matrix of a word over an alphabet has been introduced by A. Cerny (2009) in studying a property, known as fair words and it is closely related to Parikh matrix. In this paper we consider Precedence matrix for words especially over binary, ternary and tertiary alphabets and develop algorithm to display of the Precedence matrices of words.

Keywords

Ternary word, Tertiary word, subword, Precedence matrix.

References

[1] A. Cerny, On fair words Journal of Automata, Languages and Combinatorics., 14 (2), pp 163-174, 2009.
[2] A. Bhattacharjee, B. S. Purkayastha, some alternative ways to find M-ambiguous binary words corresponding to a Parikh Matrix, Int. J. of Computer Applications, Vol 4 No.1 pp 53–64, 2014.
[3] A. Bhattacharjee, B. S. Purkayastha, Parikh Matrices and Words over Ternary Ordered Alphabet P roceedings of fourth International Conference on Soft computing for Problem Solving, Vol 1(AISC, Vol 335) pp.135–145, 2014.
[4] A. Bhattacharjee, B. S. Purkayastha, Parikh Matrices and Words over Tertiary Ordered Alphabet, Int. J. of Computer Applications, Vol 85, No.4, pp10–15, 2014.
[5] A. Mateescu, A. Salomaa, K. Salomaa and S. Yu, A Sharpening of the Parikh Mapping, RAIRO-Theoretical Informatics and Applications, 35, 551-564, 2001.
[6] M. Lothaire, Combinatorics on Words, Cambridge Mathematical Library, Cambridge university Press, 1997.
[7] L. Kari and K. Mahalingam, Involutively bordered words, International Journal of Foundations of Computer Science, 18, 1089-1106, 2007.
[8] C. A. Priya Darshini, V. R. Dare, I. Venkat and K.G. Subramanian, Factors of words under an involution, Journal of Mathematics and Informatics, 1 (2013-14) 52-59.
[9] A. Mateescu and A. Salomaa, Matrix indicators for subword occurrences and ambiguity, International Journal of Foundations of Computer Science, 17, 277-292, 2004.
[10] K. Mahalingam and K. G. Subramanian, Product of Parikh Matrices and Commutativity, International Journal of Foundations of Computer Science, 23, 207-223, 2012.