## Abstract

An involution π is said to be τ-ccontain any subsequence having all the same pairwise comparisons as τ. This paper concerns the enumeration of involutions which avoid a set A _{κ} of subsequences increasing both in number and in length at the same time. Let A _{κ} be the set of all the permutations 12π _{3}.. π _{κ}. of length k. For κ = 3 the only subsequence in A _{κ} is 123 and the 123-avoiding involutions of length n are enumerated by the central binomial coefficients (n/⌊n/2]). For k = 4 we give a combinatorial explanation that shows the number of involutions of length n avoiding A _{4} is the same as the number of symmetric Schröder paths of length n-1. For each k ≥ 3 we determine the generating function for the number of involutions avoiding the subsequences in A _{κ}, according to length, first entry and number of fixed points.

Original language | English |
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State | Published - 2007 |

Event | 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 - Tianjin, China Duration: 2 Jul 2007 → 6 Jul 2007 |

### Conference

Conference | 19th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'07 |
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Country/Territory | China |

City | Tianjin |

Period | 2/07/07 → 6/07/07 |

## Keywords

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

## ASJC Scopus subject areas

- Algebra and Number Theory

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