### Abstract

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.

Language | English |
---|---|

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 |

### Fingerprint

### Keywords

- classical patterns
- ordered patterns
- morphisms

### Cite this

*Integers: Electronic Journal of Combinatorial Number Theory*,

*8*(1), [A-3].

}

*Integers: Electronic Journal of Combinatorial Number Theory*, vol. 8, no. 1, A-3.

**Counting ordered patterns in words generated by morphisms.** / Kitaev, Sergey; Mansour, Toufik; Seebold, Patrice.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Counting ordered patterns in words generated by morphisms

AU - Kitaev, Sergey

AU - Mansour, Toufik

AU - Seebold, Patrice

PY - 2008/1/29

Y1 - 2008/1/29

N2 - 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 andshowing their interest.

AB - 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 andshowing their interest.

KW - classical patterns

KW - ordered patterns

KW - morphisms

UR - https://personal.cis.strath.ac.uk/sergey.kitaev/index_files/Papers/PatternMorph.pdf

UR - http://www.westga.edu/~integers/cgi-bin/get.cgi

M3 - Article

VL - 8

JO - Integers: Electronic Journal of Combinatorial Number Theory

T2 - Integers: Electronic Journal of Combinatorial Number Theory

JF - Integers: Electronic Journal of Combinatorial Number Theory

SN - 1553-1732

IS - 1

M1 - A-3

ER -