PARIKH $\texttt{q}-$ MATRIX UNDER PROUHET MORPHISM

Print ISSN: 0972-7752 | Online ISSN: 2582-0850

Volume : 21 , Issue : Proceedings
Author :
K. Janaki (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur - 603203, Chennai)
Wen Chen Teh (School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, MALAYSIA)
R. Arulprakasam (Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur - 603203, Chennai)

Abstract

The Parikh $\texttt{q}-$matrix is the extension of Parikh matrix that maps words to matrices with polynomial entries. Since Parikh $\texttt{q}-$matrix mapping is not an injective mapping, we consider Prouhet morphism on words to distinguish $\texttt{q}-$equivalent binary words by their Parikh $\texttt{q}-$matrix. We state the formulae to calculate $\texttt{q}-$counting of scattered subwords of the image of any word under Prouhet morphism. With the aid of Parikh $\texttt{q}-$matrices, we establish various properties of image of words under this morphism.

Keywords and Phrases

Subwords, Parikh matrix, Parikh $\texttt{q}-$matrix, Prouhet morphism.

A.M.S. subject classification

68R15, 68Q45.

.....

View PDF Click here to Subscribe now