Parikh Matrices for Powers of Words
Adrian Atanasiu, Ghajendran Poovanandran, Wen Chean Teh

TL;DR
This paper explores the properties of Parikh matrices related to powers of words, introduces canonical decompositions, and establishes relations between normal forms and M-equivalence classes.
Contribution
It provides a method to compute Parikh matrices for word powers and introduces normal forms for matrices and words, enhancing combinatorial analysis tools.
Findings
Computed Parikh matrices for arbitrary word powers
Proposed canonical decompositions and normal forms
Established relations between matrix and word normal forms
Abstract
Certain upper triangular matrices, termed as Parikh matrices, are often used in the combinatorial study of words. Given a word, the Parikh matrix of that word elegantly computes the number of occurrences of certain predefined subwords in that word. In this paper, we compute the Parikh matrix of any word raised to an arbitrary power. Furthermore, we propose canonical decompositions of both Parikh matrices and words into normal forms. Finally, given a Parikh matrix, the relation between its normal form and the normal forms of words in the corresponding M-equivalence class is established.
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Algorithms and Data Compression
