Algebraic Properties of Parikh Matrices of Binary Picture Arrays

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 (Accepted for Publication)

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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: This article has been accepted for publication in the Journal of Mathematics: https://www.hindawi.com/journals/jmath/
Keywords: Combinatorics on words, Parikh Matrices, Binary Picture Arrays
Faculty / Department: Faculty of Science > Mathematics and Computer Science
Depositing User: Atulya Nagar
Date Deposited: 07 Jun 2020 14:00
Last Modified: 07 Jun 2020 14:00
URI: https://hira.hope.ac.uk/id/eprint/3079

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