Acta Informatica

, Volume 56, Issue 6, pp 521–535 | Cite as

Parikh matrices for powers of words

  • Adrian Atanasiu
  • Ghajendran Poovanandran
  • Wen Chean TehEmail author
Original Article


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.

Mathematics Subject Classification

68R15 05A05 



The second and third authors gratefully acknowledge support for this research by a Research University Grant No. 1011/PMATHS/8011019 of Universiti Sains Malaysia. This paper is a part of the second author’s Ph.D. work.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceBucharest UniversityBucharestRomania
  2. 2.School of Mathematical SciencesUniversiti Sains MalaysiaUSMMalaysia

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