Algebraic Properties of Parikh Matrices of Binary Picture Arrays Article Swipe

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Somnath Bera , S. Sriram , Atulya K. Nagar , Linqiang Pan , K. G. Subramanian ·

YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.1155/2020/3236405

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.

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Mathematics Word (group theory) Diagonal Triangular matrix Binary number Algebraic number Extension (predicate logic) Matrix (chemical analysis) Sequence (biology) Operator (biology) Combinatorics Discrete mathematics Algebra over a field Pure mathematics Arithmetic Mathematical analysis Geometry Computer science Biochemistry Programming language Materials science Gene Transcription factor Biology Composite material Genetics Invertible matrix Repressor Chemistry

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Type: article
Language: en
Landing Page: https://doi.org/10.1155/2020/3236405
PDF: https://downloads.hindawi.com/journals/jmath/2020/3236405.pdf
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Cited By: 2
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DOI: https://doi.org/10.1155/2020/3236405

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Title: Algebraic Properties of Parikh Matrices of Binary Picture Arrays

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Publication year: 2020

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Publication date: 2020-06-29

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Authors: Somnath Bera, S. Sriram, Atulya K. Nagar, Linqiang Pan, K. G. Subramanian

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Concepts: Mathematics, Word (group theory), Diagonal, Triangular matrix, Binary number, Algebraic number, Extension (predicate logic), Matrix (chemical analysis), Sequence (biology), Operator (biology), Combinatorics, Discrete mathematics, Algebra over a field, Pure mathematics, Arithmetic, Mathematical analysis, Geometry, Computer science, Biochemistry, Programming language, Materials science, Gene, Transcription factor, Biology, Composite material, Genetics, Invertible matrix, Repressor, Chemistry

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Cited by: 2

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