Records in set partitions

Arnold Knopfmacher, Toufik Mansour, Stephan Wagner

Research output: Contribution to journalArticlepeer-review


A partition of [n] = {1,2,..., n} is a decomposition of [n] into nonempty subsets called blocks. We will make use of the canonical representation of a partition as a word over a finite alphabet, known as a restricted growth function. An element ai in such a word π is a strong (weak) record if ai > aj (ai ≥ aj) 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 words corresponding to partitions of [n], as well as for the sum of the positions of the records. In addition we find the asymptotic mean values and variances for the number, and for the sum of positions, of strong (weak) records in all partitions of [n].

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalElectronic Journal of Combinatorics
Issue number1
StatePublished - 2010

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


Dive into the research topics of 'Records in set partitions'. Together they form a unique fingerprint.

Cite this