Record statistics in a random composition

Arnold Knopfmacher, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


A composition σ=a 1a 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 languageEnglish
Pages (from-to)593-603
Number of pages11
JournalDiscrete Applied Mathematics
Issue number4-5
StatePublished - Mar 2012

Bibliographical note

Funding Information:
This material is based upon work supported by the National Research Foundation under grant number 2053740 .


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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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