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A Permutation on Words in a Two Letter Alphabet

  • Niccolò Castronuovo
  • Robert Cori
  • Sébastien Labbé
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10432)

Abstract

We define a permutation \(\varGamma _n\) on the set of words with n occurrences of the letter a and \(n+1\) occurrences of the letter b. The definition of this permutation is based on a factorization of these words that allows to associate a non crossing partition to them. We prove that all the cycles of this permutation are of odd lengths. We will prove also other properties of this permutation \(\varGamma _n\), one of them allows to build a family of strips of stamps.

Keywords

Dyck words Permutations Strips of stamps 

Notes

Acknowledgement

We are very grateful for the many valuable comments of the reviewers which improved the article presentation.

References

  1. 1.
    Armstrong, C., Mingo, J.A., Speicher, R., Wilson, J.C.H.: The non-commutative cycle lemma. J. Combin. Theory Ser. A 117(8), 1158–1166 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Barnabei, M., Bonetti, F., Castronuovo, N., Cori, R.: Some permutations on Dyck words. Theoret. Comput. Sci. 635, 51–63 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Baumert, L.D.: Cyclic Difference Sets. LNM, vol. 182. Springer, Heidelberg (1971). doi: 10.1007/BFb0061260 zbMATHGoogle Scholar
  4. 4.
    Chottin, L., Cori, R.: Une preuve combinatoire de la rationalité d’une série génératrice associée aux arbres. RAIRO Inform. Théor. 16(2), 113–128 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Cori, R., Hetyei, G.: Counting genus one partitions and permutations. Sém. Lothar. Combin. 70, 29 (2013). Art. B70eMathSciNetzbMATHGoogle Scholar
  6. 6.
    Di Francesco, P., Golinelli, O., Guitter, E.: Meanders: a direct enumeration approach. Nucl. Phys. B 482(3), 497–535 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Dvoretzky, A., Motzkin, T.: A problem of arrangements. Duke Math. J. 14, 305–313 (1947)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lando, S.K., Zvonkin, A.K.: Plane and projective meanders. Theoret. Comput. Sci. 117(1–2), 227–241 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Legendre, S.: Foldings and meanders. Australas. J. Combin. 58, 275–291 (2014)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Lothaire, M.: Combinatorics on words. In: Encyclopedia of Mathematics and its Applications, vol. 17. Addison-Wesley Publishing Co., Reading (1983)Google Scholar
  11. 11.
    Lothaire, M.: Algebraic combinatorics on words. In: Encyclopedia of Mathematics and its Applications, vol. 90. Cambridge University Press, Cambridge (2002)Google Scholar
  12. 12.
    Storer, T.: Cyclotomy and difference sets. In: Lectures in Advanced Mathematics, no. 2. Markham Publishing Co., Chicago (1967)Google Scholar
  13. 13.
    Touchard, J.: Contribution à l’étude du problème des timbres poste. Can. J. Math. 2, 385–398 (1950)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Niccolò Castronuovo
    • 1
  • Robert Cori
    • 2
  • Sébastien Labbé
    • 3
  1. 1.Dipartimento di MatematicaUniversità di FerraraFerraraItaly
  2. 2.LaBRIUniversité de BordeauxBordeauxFrance
  3. 3.CNRS, LaBRI, UMR 5800TalenceFrance

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