Arnold Knopfmacher ; Toufik Mansour - Record statistics in integer compositions

dmtcs:2691 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2691
Record statistics in integer compositionsConference paper

Authors: Arnold Knopfmacher ORCID1; Toufik Mansour ORCID2

  • 1 The John Knopfmacher Centre for Applicable Analysis and Number Theory [Johannesburg]
  • 2 Department of Mathematics [Haïfa]

A composition σ=a1a2am of n is an ordered collection of positive integers whose sum is n. An element ai in σ is a strong (weak) record if ai>aj(aiaj) for all j=1,2,,i1. 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 ai 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.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: Composition,Record,Left-to-right maxima,Generating function,Mellin transforms,Asymptotic estimates,[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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