## Abstract

We prove that every sufficiently long simple permutation contains two long almost disjoint simple subsequences, and then we show how this result has enumerative consequences. For example, it implies that, for any r, the number of permutations with at most r copies of 132 has an algebraic generating function (this was previously proved, constructively, by Bóna and (independently) Mansour and Vainshtein).

Translated title of the contribution | Decomposing simple permutations, with enumerative consequences |
---|---|

Original language | English |

Pages (from-to) | 385 - 400 |

Number of pages | 16 |

Journal | Combinatorica |

Volume | 28 (4) |

DOIs | |

Publication status | Published - Jul 2008 |