Malaysian Journal of Mathematical Sciences, April 2019, Vol. 13(S)
Special Issue: 3rd International Conference on Mathematical Sciences and Statistics (ICMSS2018)
Algebraic Properties of Parikh Matrices of Words under an Extension of Thue Morphism
Subramanian, K. G., Sriram, S., Prasanna Venkatesan, A. S., and Nagar, A. K.
Corresponding Email: [email protected]
Received date: -
Accepted date: -
Abstract:
The Parikh matrix of a word \(w\) over an alphabet \(\left \{ a_1,...,a_k \right \}\) with an ordering \(a_1 < a_2 < ...a_k\) gives the number of occurrences of each factor of the word \( a_1...a_k\) as a (scattered) subword of the word \(w\). Two words \(u,v\) are said to be \(M\)-equivalent, if the Parikh matrices of \(u\) and \(v\) are the same. Here an extension to three letters, of the well-known Thue morphism on two letters introduced by S\(\acute{e}\acute{e}\)bold (2003), is considered and the properties of Parikh matrices of morphic images of words are
investigated. The significance of the contribution is that various classes of binary words are obtained whose images are \(M\)-equivalent under this extended morphism.
Keywords: Morphic image of a word, Parikh matrix of a word, Thue morphism
