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Counting ordered patterns in words generated by morphisms

Patrice Séébold 1, 2, * Sergey Kitaev 3 Toufik Mansour 4 
* Corresponding author
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : 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.
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Submitted on : Wednesday, July 29, 2009 - 12:03:03 AM
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Patrice Séébold, Sergey Kitaev, Toufik Mansour. Counting ordered patterns in words generated by morphisms. LATA'2008: 2nd International Conference on Language and Automata Theory and Applications, Mar 2008, Tarragona, Spain. pp.287-298. ⟨lirmm-00408114⟩



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