### Abstract

subsequence of π whose letters are in the same relative order (of size) as those

in p. In an occurrence of a generalized pattern, some letters of that subsequence

may be required to be adjacent in the permutation. Subsets of permutations

characterized by the avoidance—or the prescribed number of occurrences—

of generalized patterns exhibit connections to an enormous variety of other

combinatorial structures, some of them apparently deep. We give a short

overview of the state of the art for generalized patterns.

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

Pages | 137–152 |

Number of pages | 16 |

Journal | London Mathematical Society Lecture Note Series |

Publication status | Published - 2010 |

### Fingerprint

### Keywords

- permutation
- pat- tern avoidance
- Generalized permutation patterns
- pattern

### Cite this

}

**Generalized permutation patterns - a short survey.** / Steingrimsson, Einar.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Generalized permutation patterns - a short survey

AU - Steingrimsson, Einar

PY - 2010

Y1 - 2010

N2 - An occurrence of a classical pattern p in a permutation π is asubsequence of π whose letters are in the same relative order (of size) as thosein p. In an occurrence of a generalized pattern, some letters of that subsequencemay be required to be adjacent in the permutation. Subsets of permutationscharacterized by the avoidance—or the prescribed number of occurrences—of generalized patterns exhibit connections to an enormous variety of othercombinatorial structures, some of them apparently deep. We give a shortoverview of the state of the art for generalized patterns.

AB - An occurrence of a classical pattern p in a permutation π is asubsequence of π whose letters are in the same relative order (of size) as thosein p. In an occurrence of a generalized pattern, some letters of that subsequencemay be required to be adjacent in the permutation. Subsets of permutationscharacterized by the avoidance—or the prescribed number of occurrences—of generalized patterns exhibit connections to an enormous variety of othercombinatorial structures, some of them apparently deep. We give a shortoverview of the state of the art for generalized patterns.

KW - permutation

KW - pat- tern avoidance

KW - Generalized permutation patterns

KW - pattern

M3 - Article

SP - 137

EP - 152

JO - London Mathematical Society Lecture Note Series

T2 - London Mathematical Society Lecture Note Series

JF - London Mathematical Society Lecture Note Series

SN - 0076-0552

ER -