Back to Search
Start Over
Algebraic Properties of Parikh Matrices of Binary Picture Arrays
- Source :
- Journal of Mathematics, Vol 2020 (2020)
- Publication Year :
- 2020
- Publisher :
- Wiley, 2020.
-
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 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.
- Subjects :
- Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 23144629 and 23144785
- Volume :
- 2020
- Database :
- Directory of Open Access Journals
- Journal :
- Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.5685bae424c8438c842a513947c5fbf4
- Document Type :
- article
- Full Text :
- https://doi.org/10.1155/2020/3236405