Counting ordered patterns in words generated by morphisms

Sergey Kitaev, Toufik Mansour, Patrice Seebold

Research output: Contribution to journalArticlepeer-review


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 those 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.
Original languageEnglish
Article numberA-3
Number of pages28
JournalIntegers: Electronic Journal of Combinatorial Number Theory
Issue number1
Publication statusPublished - 29 Jan 2008


  • classical patterns
  • ordered patterns
  • morphisms


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