A finite sequence, called a word, has its terms belonging to a finite set of symbols. Words are basic objects in formal language theoretic studies. Around the year 2000, Mateescu et al. formulated the notion of Parikh matrix of a word. Several investigations on images of words and properties of Parikh matrices of these words under various morphisms have taken place. The notion of Parikh matrix has also been extended to two-dimensional (2D) picture arrays that are rectangular arrangements of symbols. Here we consider Prouhet array morphism and obtain certain properties relating to Parikh matrix of the image of a 2D picture array under Prouhet array morphism, thereby enriching the study of combinatorial properties of two-dimensional picture arrays.

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Parikh Matrices of Prouhet Array Morphic Images of Two-Dimensional Arrays

  • R. Stella Maragatham,
  • V. Nithya Vani

摘要

A finite sequence, called a word, has its terms belonging to a finite set of symbols. Words are basic objects in formal language theoretic studies. Around the year 2000, Mateescu et al. formulated the notion of Parikh matrix of a word. Several investigations on images of words and properties of Parikh matrices of these words under various morphisms have taken place. The notion of Parikh matrix has also been extended to two-dimensional (2D) picture arrays that are rectangular arrangements of symbols. Here we consider Prouhet array morphism and obtain certain properties relating to Parikh matrix of the image of a 2D picture array under Prouhet array morphism, thereby enriching the study of combinatorial properties of two-dimensional picture arrays.