### Abstract

An occurrence of a classical pattern p in a permutation π is a

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.

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.

Original language | English |
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Pages (from-to) | 137–152 |

Number of pages | 16 |

Journal | London Mathematical Society Lecture Note Series |

Publication status | Published - 2010 |

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### Keywords

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