## Abstract

A permutation π is said to be a Dumont permutation of the first kind if each even integer in π must be followed by a smaller integer, and each odd integer is either followed by a larger integer or is the last element of π (see, for example, www.theory.csc.uvic.ca/~cos/inf/perm/Genocchi Info.html). In Duke Math. J. 41 (1974), 305-318, Dumont showed that certain classes of permutations on n letters are counted by the Genocchi numbers. In particular, Dumont showed that the (n + 1)st Genocchi number is the number of Dummont permutations of the first kind on 2n letters. In this paper we study the number of Dumont permutations of the first kind on n letters avoiding the pattern 132 and avoiding (or containing exac tly once) an arbitrary pattern on k letters. In several interesting cases the generating function depends only on k.

Original language | English |
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Pages (from-to) | 103-117 |

Number of pages | 15 |

Journal | Australasian Journal of Combinatorics |

Volume | 29 |

State | Published - 2004 |

Externally published | Yes |

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics