Research Output per year

### Abstract

The class Av(1324), of permutations avoiding the pattern 1324, is one of the simplest sets of combinatorial objects to define that has, thus far, failed to reveal its enumerative secrets. By considering certain large subsets of the class, which consist of permutations with a particularly regular structure, we prove that the growth rate of the class exceeds 9.81. This improves on a previous lower bound of 9.47. Central to our proof is an examination of the asymptotic distributions of certain substructures in the Hasse graphs of the permutations. In this context, we consider occurrences of patterns in Łukasiewicz paths and prove that in the limit they exhibit a concentrated Gaussian distribution.

Original language | English |
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Pages (from-to) | 105–122 |

Number of pages | 18 |

Journal | Journal of the London Mathematical Society |

Volume | 92 |

Issue number | 1 |

Early online date | 16 Jun 2015 |

DOIs | |

Publication status | Published - 31 Aug 2015 |

### Keywords

- permutations
- permutation classes
- Av(3124)
- Łukasiewicz paths

## Fingerprint Dive into the research topics of 'Permutations avoiding 1324 and patterns in Łukasiewicz paths'. Together they form a unique fingerprint.

## Profiles

## Research Output

- 8 Citations
- 1 Doctoral Thesis

## On the growth of permutation classes

Bevan, D., 1 Jun 2015, Milton Keynes.Research output: Thesis › Doctoral Thesis