Bera, Somnath and Sriram, Sastha and Nagar, Atulya K. and Pan, Linqiang and Subramanian, K.G. (2020) Algebraic Properties of Parikh Matrices of Binary Picture Arrays. Journal of Mathematics. ISSN 2314-4785
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Abstract
A word is a finite sequence of symbols. Parikh matrix of a word is an upper triangular matrix with ones in the main diagonal and non-negative integers above the main diagonal which are counts of certain scattered subwords in the word. On the other hand a picture array, which is a rectangular arrangement of symbols, is an extension of the notion of word to two dimensions. Parikh matrices associated with a picture array have been introduced and their properties have been studied. Here we obtain certain algebraic properties of Parikh matrices of binary picture arrays based on the notions of power, fairness and a restricted shuffle operator extending the corresponding notions studied in the case of words. We also obtain properties of Parikh matrices of arrays formed by certain geometric operations.
| Item Type: | Article |
|---|---|
| Additional Information and Comments: | Copyright © 2020 Somnath Bera et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | Combinatorics on words, Parikh Matrices, Binary Picture Arrays |
| Faculty / Department: | Faculty of Human and Digital Sciences > School of Computer Science and the Environment |
| Depositing User: | Atulya Nagar |
| Date Deposited: | 07 Jun 2020 14:00 |
| Last Modified: | 10 Mar 2025 11:59 |
| URI: | https://hira.hope.ac.uk/id/eprint/3079 |
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