### Abstract

Original language | English |
---|---|

Pages (from-to) | 4108-4115 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 309 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- Schröder paths
- restricted involutions
- mathematics

### Cite this

*Discrete Mathematics*,

*309*(12), 4108-4115. https://doi.org/10.1016/j.disc.2008.12.011

}

*Discrete Mathematics*, vol. 309, no. 12, pp. 4108-4115. https://doi.org/10.1016/j.disc.2008.12.011

**Symmetric Schröder paths and restricted involutions.** / Dukes, W.M.B.; Deng, Eva; Mansour, Toufik; Wu, Susan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Symmetric Schröder paths and restricted involutions

AU - Dukes, W.M.B.

AU - Deng, Eva

AU - Mansour, Toufik

AU - Wu, Susan

PY - 2009

Y1 - 2009

N2 - Let Ak be the set of permutations in the symmetric group Sk with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns Ak. We present a bijection between symmetric Schroder paths of length $2n and involutions of length n+1 avoiding mathcalA4. 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 Schroder path of a particular type. For each k> 2 we determine the generating function for the number of involutions avoiding the subsequences in Ak, according to length, first entry and number of fixed points.

AB - Let Ak be the set of permutations in the symmetric group Sk with prefix 12. This paper concerns the enumeration of involutions which avoid the set of patterns Ak. We present a bijection between symmetric Schroder paths of length $2n and involutions of length n+1 avoiding mathcalA4. 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 Schroder path of a particular type. For each k> 2 we determine the generating function for the number of involutions avoiding the subsequences in Ak, according to length, first entry and number of fixed points.

KW - Schröder paths

KW - restricted involutions

KW - mathematics

UR - http://arxiv.org/abs/0810.5189

U2 - 10.1016/j.disc.2008.12.011

DO - 10.1016/j.disc.2008.12.011

M3 - Article

VL - 309

SP - 4108

EP - 4115

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 12

ER -