## Abstract

Let A_{k} be the set of permutations in the symmetric group S_{k} with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns A_{k}. We present a bijection between symmetric Schröder paths of length 2 n and involutions of length n + 1 avoiding A_{4}. Statistics such as the number of right-to-left maxima and fixed points of the involution correspond to the number of steps in the symmetric Schröder path of a particular type. For each k ≥ 3 we determine the generating function for the number of involutions avoiding the subsequences in A_{k}, according to length, first entry and number of fixed points.

Original language | English |
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Pages (from-to) | 4108-4115 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 309 |

Issue number | 12 |

DOIs | |

State | Published - 28 Jun 2009 |

## Keywords

- Forbidden subsequences
- Involutions
- Schröder paths
- Symmetric Schröder paths

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics