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International Conference on Combinatorics on Words

WORDS 2019: Combinatorics on Words pp 68–79Cite as

Parikh Determinants

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11682))

Abstract

Parikh matrices, introduced by Mateescu et al. in 2001, are generalization of the classical Parikh vectors. These special matrices are often utilized in the combinatorial study of words as an elegant tool to compute the number of occurrences of certain subwords in a word. In this paper, we study the determinant of a certain submatrix of a Parikh matrix, where the submatrix preserves the information contained in the original matrix. We present a formula to compute such a determinant, which we term as the Parikh determinant, for any given word. By using a classical result on Parikh matrices, we establish Parikh determinants as a natural combinatorial characteristic of words. Consequently, a new general identity involving the number of occurrences of certain subwords of a word is obtained. Finally, we address some related observations and possible future directions of this study.

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Acknowledgements

This work was completed during the sabbatical leave of the third author from 15 Nov 2018 to 14 Aug 2019, supported by Universiti Sains Malaysia.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Bucharest University, Str. Academiei 14, 010014, Bucharest, Romania

    Adrian Atanasiu

  2. School of Mathematics, Actuarial and Quantitative Studies, Asia Pacific University of Technology & Innovation, Technology Park Malaysia, 57000, Bukit Jalil, Kuala Lumpur, Malaysia

    Ghajendran Poovanandran

  3. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, USM, Malaysia

    Wen Chean Teh

Authors
  1. Adrian Atanasiu
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  2. Ghajendran Poovanandran
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  3. Wen Chean Teh
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Corresponding author

Correspondence to Ghajendran Poovanandran .

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Editors and Affiliations

  1. Loughborough University, Loughborough, UK

    Robert Mercaş

  2. Loughborough University, Loughborough, UK

    Daniel Reidenbach

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Atanasiu, A., Poovanandran, G., Teh, W.C. (2019). Parikh Determinants. In: Mercaş, R., Reidenbach, D. (eds) Combinatorics on Words. WORDS 2019. Lecture Notes in Computer Science(), vol 11682. Springer, Cham. https://doi.org/10.1007/978-3-030-28796-2_5

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  • DOI: https://doi.org/10.1007/978-3-030-28796-2_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-28795-5

  • Online ISBN: 978-3-030-28796-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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