Extensions of Parikh matrix of a word to a two-dimensional binary word

Bera, Somnath and Nagar, Atulya K. and Subramanian, K.G. (2024) Extensions of Parikh matrix of a word to a two-dimensional binary word. Journal of Automata, Languages and Combinatorics. ISSN 2567-3785 (Accepted for Publication)

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Abstract

The concept of Parikh matrix of a word was introduced based on the counts of scattered subwords (also called subwords) in a word and many interesting properties have been established in several studies of words. The notion of Parikh matrix was then considered for a two-dimensional word (also called picture array) using counts of scattered subwords in the rows/columns of a picture array. Here we introduce two other approaches in extending the notion of subword counting and the Parikh matrix of a binary word to a two-dimensional binary word and obtain certain combinatorial properties in both the approaches. A simple bipartite graph has also been associated with a word based on subwords. We also introduce corresponding graphs for a two-dimensional binary word again based on subword counting in the approaches considered here.

Item Type:	Article
Additional Information and Comments:	Accepted for publication in the Journal of Automata, Languages and Combinatorics. The final, published version will be available from: https://jalc.de/
Keywords:	Two-dimensional word, scattered subword, Parikh matrix
Faculty / Department:	Faculty of Human and Digital Sciences > Mathematics and Computer Science
Depositing User:	Atulya Nagar
Date Deposited:	03 Jun 2024 09:02
Last Modified:	03 Jun 2024 09:02
URI:	https://hira.hope.ac.uk/id/eprint/4278

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