## Abstract

A composition σ = a _{1}a _{2}. .. a _{m} of n is an ordered collection of positive integers whose sum is n. An element ai in σ is a strong (weak) record if a _{i} > a _{j} (a _{i} ≥ a _{j} ) for all j = 1; 2;. . ., i - 1. Furthermore, the position of this record is i. We derive generating functions for the total number of strong (weak) records in all compositions of n, as well as for the sum of the positions of the records in all compositions of n, where the parts a _{i} belong to a fixed subset A of the natural numbers. In particular when A = ℕ, we find the asymptotic mean values for the number, and for the sum of positions, of records in compositions of n.

Original language | English |
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Pages | 527-536 |

Number of pages | 10 |

State | Published - 2009 |

Event | 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 - Linz, Austria Duration: 20 Jul 2009 → 24 Jul 2009 |

### Conference

Conference | 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 |
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Country/Territory | Austria |

City | Linz |

Period | 20/07/09 → 24/07/09 |

## Keywords

- Asymptotic estimates
- Composition
- Generating function
- Left-to-right maxima
- Mellin transforms
- Record

## ASJC Scopus subject areas

- Algebra and Number Theory