Algebraic Properties of Parikh Matrices of Binary Picture Arrays

Autor: Somnath Bera, Sastha Sriram, Atulya K. Nagar, Linqiang Pan, K. G. Subramanian
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Journal of Mathematics, Vol 2020 (2020)
Druh dokumentu: article
ISSN: 2314-4629
2314-4785
DOI: 10.1155/2020/3236405
Popis: 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 nonnegative 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 a 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.
Databáze: Directory of Open Access Journals
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