# Upper bounds for the Stanley–Wilf limit of 1324 and other layered patterns

Claesson, Anders and Jelínek, Vít and Steingrimsson, Einar
(2012)
*Upper bounds for the Stanley–Wilf limit of 1324 and other layered patterns.*
Journal of Combinatorial Theory Series A, 119 (8).
pp. 1680-1691.
ISSN 0097-3165

## Abstract

We prove that the Stanley-Wilf limit of any layered permutation pattern of length l is at most 4l(2), and that the Stanley-Wilf limit of the pattern 1324 is at most 16. These bounds follow from a more general result showing that a permutation avoiding a pattern of a special form is a merge of two permutations, each of which avoids a smaller pattern. We also conjecture that, for any k >= 0, the set of 1324-avoiding permutations with k inversions contains at least as many permutations of length n + 1 as those of length n. We show that if this is true then the Stanley-Wilf limit for 1324 is at most e(pi root 2/3) similar or equal to 13.001954.

Item type: | Article |
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ID code: | 42133 |

Keywords: | upper bounds , stanley-wilf limit , layered patterns, pattern avoidance, layered permutations , Electronic computers. Computer science, Discrete Mathematics and Combinatorics, Computational Theory and Mathematics, Theoretical Computer Science |

Subjects: | Science > Mathematics > Electronic computers. Computer science |

Department: | Faculty of Science > Computer and Information Sciences |

Depositing user: | Pure Administrator |

Date Deposited: | 19 Nov 2012 14:20 |

Last modified: | 04 May 2016 22:51 |

URI: | http://strathprints.strath.ac.uk/id/eprint/42133 |