## Abstract

We use the Mansour-Vainshtein theory of kernel shapes [14] to decompose the set S_{n}(1324) of 1324-avoiding permutations of length n into small pieces that are governed by some kernel shape λ. An enumeration of the set K_{m,c} of all kernel shapes with length m and capacity c allows to express the generating function for the number of 1324-avoiding permutations of length n in terms of the P_{m}(C(x))=∑_{c}|K_{m,c+1}|C^{c}(x) where P_{m}(x) is a polynomial and C(x) is the generating function for the Catalan numbers. This allows us to write down a systematic procedure for finding a lower bound for approximating the Stanley-Wilf limit of the pattern 1324. We use an implementation of this method in the OpenCL framework to compute such a bound explicitly.

Original language | English |
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Article number | 102229 |

Journal | Advances in Applied Mathematics |

Volume | 130 |

DOIs | |

State | Published - Sep 2021 |

### Bibliographical note

Funding Information:We would like to thank G?khan Y?ld?r?m and Tony Guttmann for discussions of an earlier version of the manuscript. The computations presented in this work were performed on the Hive computer cluster at the University of Haifa.

Publisher Copyright:

© 2021 Elsevier Inc.

## Keywords

- 1324-avoiding permutations
- Generating functions
- Occurrences of 132

## ASJC Scopus subject areas

- Applied Mathematics