### 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 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.

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 language | English |
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Article number | A-3 |

Number of pages | 28 |

Journal | Integers: Electronic Journal of Combinatorial Number Theory |

Volume | 8 |

Issue number | 1 |

Publication status | Published - 29 Jan 2008 |

### Keywords

- classical patterns
- ordered patterns
- morphisms

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## Cite this

Kitaev, S., Mansour, T., & Seebold, P. (2008). Counting ordered patterns in words generated by morphisms.

*Integers: Electronic Journal of Combinatorial Number Theory*,*8*(1), [A-3].