## 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 a _{i} 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=[d]:=1,2,...,d or A=N. 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 | American English |
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Pages (from-to) | 593-603 |

Number of pages | 11 |

Journal | Discrete Applied Mathematics |

Volume | 160 |

Issue number | 4-5 |

DOIs | |

State | Published - Mar 2012 |

## Keywords

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

## All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics