Counting Ordered Patterns in Words Generated by Morphisms

  • Sergey Kitaev
  • Toufik Mansour
  • Patrice Séébold
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5196)


We start a general study of counting the number of occurrences of ordered patterns in words generated by morphisms. We consider certain patterns with gaps (classical patterns) and that with no gaps (consecutive patterns). Occurrences of the patterns are known, in the literature, as rises, descents, (non-)inversions, squares and p-repetitions. We give recurrence formulas in the general case, then deducing exact formulas for particular families of morphisms. Many (classical or new) examples are given illustrating the techniques and showing their interest.


Morphisms patterns rises descents inversions repetitions 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sergey Kitaev
    • 1
  • Toufik Mansour
    • 2
  • Patrice Séébold
    • 3
  1. 1.Reykjavík UniversityReykjavíkIceland
  2. 2.Department of MathematicsHaifa UniversityHaifaIsrael
  3. 3.LIRMMUniv. Montpellier 2, CNRSMontpellierFrance

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