Skip to Main content Skip to Navigation
Conference papers

Record statistics in integer compositions

Abstract : A $\textit{composition}$ $\sigma =a_1 a_2 \ldots a_m$ of $n$ is an ordered collection of positive integers whose sum is $n$. An element $a_i$ in $\sigma$ is a strong (weak) $\textit{record}$ if $a_i> a_j (a_i \geq a_j)$ for all $j=1,2,\ldots,i-1$. 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 $A=\mathbb{N}$, we find the asymptotic mean values for the number, and for the sum of positions, of records in compositions of $n$.
Complete list of metadata

Cited literature [14 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 20, 2015 - 11:06:52 AM
Last modification on : Wednesday, February 20, 2019 - 4:32:10 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 9:54:38 AM


Publisher files allowed on an open archive


  • HAL Id : hal-01185383, version 1



Arnold Knopfmacher, Toufik Mansour. Record statistics in integer compositions. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.527-536. ⟨hal-01185383⟩



Record views


Files downloads