Algebraic Properties of Parikh Matrices of Words under an Extension of Thue Morphism

Subramanian, K.G. and Sriram, S. and Venkatesan, A.S. Prasanna and Nagar, Atulya K. (2018) Algebraic Properties of Parikh Matrices of Words under an Extension of Thue Morphism. ICMSS 2018 Conference Proceedings: Journal of Physics: Conference Series. ISSN 1742-6588 (Accepted for Publication)

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Abstract

The Parikh matrix of a word $w$ over an alphabet $\{a_1, \cdots , a_k \}$ with an ordering $a_1 < a_2 < \cdots a_k,$ gives the number of occurrences of each factor of the word $a_1 \cdots a_k$ 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. On the other hand properties of image words under different morphisms have been studied in the context of subwords and Parikh matrices. Here an extension to three letters, introduced by S$\acute{e}\acute{e}$bold (2003), of the well-known Thue morphism on two letters, is considered and 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.

Item Type: Article
Additional Information and Comments: This is the author's version of an article accepted for publication in Journal of Physics: Conference Series. When published, the final version will be available at http://iopscience.iop.org/journal/1742-6596
Keywords: Combinatorics on words; Parikh matrix; Thue Morphism
Faculty / Department: Faculty of Science > Mathematics and Computer Science
Depositing User: Atulya Nagar
Date Deposited: 16 Apr 2018 11:06
Last Modified: 16 Apr 2018 11:06
URI: http://hira.hope.ac.uk/id/eprint/2440

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