Counting Ordered Patterns in Words Generated by Morphisms

Authors:
Sergey Kitaev;Toufik Mansour;Patrice Séébold
Affiliations:
Reykjavík University, Reykjavík, Iceland 103;Department of Mathematics, Haifa University, Haifa, Israel 31905;LIRMM, Univ. Montpellier 2, CNRS, Montpellier, France 34392
Venue:
Language and Automata Theory and Applications
Year:
2008

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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.