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Lyndon Partial Words and Arrays with Applications

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Combinatorial Image Analysis (IWCIA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13348))

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Abstract

Lyndon words have been extensively studied in different contexts of free Lie algebra and combinatorics. We introduce Lyndon partial words, arrays and trees. We also study free monoid morphisms that preserve finite Lyndon partial words and check whether a morphism preserves or does not preserve the lexicographic order. We propose an algorithm to determine Lyndon partial words of given length over the binary alphabet. Image analysis in several way of scanning via automata and grammars has a significance in two-dimensional models, we connect 2D Lyndon partial words with few automata and grammar models.

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Acknowledgements

We would like to thank the unknown referees for their comments and suggestions on the manuscript in improving from an earlier version. The corresponding authors R. Krishna Kumari and R. Arulprakasam are very much thankful to the management, SRM Institute of Science and Technology for their continuous support and encouragement. Meenakshi Paramasivan would like to thank the financial support provided by CIRT (Center for Informatics Research and Technology) - University of Trier, Germany for the Celtic Studies in 2017–2018. The authors owe a big thanks to Prof. Rani Siromoney and her co-authors.

Author information

Authors and Affiliations

  1. FB IV - Informatikwissenschaften, Universität Trier, 54286, Trier, Germany

    Meenakshi Paramasivan

  2. Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chennai, 603203, India

    R. Krishna Kumari & R. Arulprakasam

  3. Department of Mathematics, Madras Christian College, Chennai, 600059, India

    V. Rajkumar Dare

Authors
  1. Meenakshi Paramasivan
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  2. R. Krishna Kumari
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  3. R. Arulprakasam
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  4. V. Rajkumar Dare
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Corresponding authors

Correspondence to R. Krishna Kumari or R. Arulprakasam .

Editor information

Editors and Affiliations

  1. State University of New York at Fredonia, Fredonia, NY, USA

    Reneta P. Barneva

  2. SUNY Buffalo State College, Buffalo, NY, USA

    Valentin E. Brimkov

  3. University of Messina, Messina, Italy

    Giorgio Nordo

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Paramasivan, M., Krishna Kumari, R., Arulprakasam, R., Dare, V.R. (2023). Lyndon Partial Words and Arrays with Applications. In: Barneva, R.P., Brimkov, V.E., Nordo, G. (eds) Combinatorial Image Analysis. IWCIA 2022. Lecture Notes in Computer Science, vol 13348. Springer, Cham. https://doi.org/10.1007/978-3-031-23612-9_14

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  • DOI: https://doi.org/10.1007/978-3-031-23612-9_14

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  • Print ISBN: 978-3-031-23611-2

  • Online ISBN: 978-3-031-23612-9

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