## 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

Publisher Copyright:© 2021 Elsevier Inc.

## Keywords

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

## ASJC Scopus subject areas

- Applied Mathematics