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On the Number of Abelian Bordered Words

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Developments in Language Theory (DLT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7907))

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Abstract

In the literature, many bijections between (labeled) Motzkin paths and various other combinatorial objects are studied. We consider abelian (un)bordered words and show the connection with irreducible symmetric Motzkin paths and paths in ℤ not returning to the origin. This study can be extended to abelian unbordered words over an arbitrary alphabet and we derive expressions to compute the number of these words. In particular, over a 3-letter alphabet, the connection with paths in the triangular lattice is made. Finally, we study the lengths of the abelian unbordered factors occurring in the Thue–Morse word.

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Author information

Authors and Affiliations

  1. Dept. of Math. and Statistics, University of Winnipeg, 515 Portage Ave., Winnipeg, MB, R3B 2E9, Canada

    Narad Rampersad

  2. Dept. of Math., University of Liège, Grande traverse 12 (B37), B-4000, Liège, Belgium

    Michel Rigo & Pavel Salimov

  3. Sobolev Institute of Math., 4 Acad. Koptyug avenue, 630090, Novosibirsk, Russia

    Pavel Salimov

Authors
  1. Narad Rampersad
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  2. Michel Rigo
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  3. Pavel Salimov
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Editor information

Editors and Affiliations

  1. LIGM, University Paris-Est Marne-la-Vallée, 5 Bd Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée Cedex 2, France

    Marie-Pierre Béal

  2. LIAFA, UMR 7089, University Paris Diderot, 75205, Paris cedex 13, France

    Olivier Carton

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Rampersad, N., Rigo, M., Salimov, P. (2013). On the Number of Abelian Bordered Words. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_37

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  • DOI: https://doi.org/10.1007/978-3-642-38771-5_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38770-8

  • Online ISBN: 978-3-642-38771-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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