### Abstract

Original language | English |
---|---|

Title of host publication | Surveys in Combinatorics 2013 |

Editors | Simon R. Blackburn, Stefanie Gerke, Mark Wildon |

Pages | 239-263 |

Number of pages | 25 |

Publication status | Published - 2013 |

### Publication series

Name | London Mathematical Society Lecture Note Series |
---|---|

Publisher | Cambridge University Press |

Volume | 409 |

### Fingerprint

### Keywords

- permutation patterns
- permutation patterns theory
- posets

### Cite this

*Surveys in Combinatorics 2013*(pp. 239-263). (London Mathematical Society Lecture Note Series; Vol. 409).

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*Surveys in Combinatorics 2013.*London Mathematical Society Lecture Note Series, vol. 409, pp. 239-263.

**Some open problems on permutation patterns.** / Steingrimsson, Einar.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Some open problems on permutation patterns

AU - Steingrimsson, Einar

PY - 2013

Y1 - 2013

N2 - This is a brief survey of some open problems on permutation patterns, with an emphasis on subjects not covered in the recent book by Kitaev, \emph{Patterns in Permutations and words}. I first survey recent developments on the enumeration and asymptotics of the pattern 1324, the last pattern of length 4 whose asymptotic growth is unknown, and related issues such as upper bounds for the number of avoiders of any pattern of length k for any given k. Other subjects treated are the M\"obius function, topological properties and other algebraic aspects of the poset of permutations, ordered by containment, and also the study of growth rates of permutation classes.

AB - This is a brief survey of some open problems on permutation patterns, with an emphasis on subjects not covered in the recent book by Kitaev, \emph{Patterns in Permutations and words}. I first survey recent developments on the enumeration and asymptotics of the pattern 1324, the last pattern of length 4 whose asymptotic growth is unknown, and related issues such as upper bounds for the number of avoiders of any pattern of length k for any given k. Other subjects treated are the M\"obius function, topological properties and other algebraic aspects of the poset of permutations, ordered by containment, and also the study of growth rates of permutation classes.

KW - permutation patterns

KW - permutation patterns theory

KW - posets

UR - http://www.cambridge.org/gb/academic/subjects/mathematics/discrete-mathematics-information-theory-and-coding/surveys-combinatorics-2013?format=PB

M3 - Chapter

SN - 9781107651951

T3 - London Mathematical Society Lecture Note Series

SP - 239

EP - 263

BT - Surveys in Combinatorics 2013

A2 - Blackburn, Simon R.

A2 - Gerke, Stefanie

A2 - Wildon, Mark

ER -