Counting 1 × 2 rectangles in set partitions

Nenad Cakić, Toufik Mansour, Armend Sh Shabani

Research output: Contribution to journalArticlepeer-review


In this paper, we study the generating function for the number of partitions of [n] = {1, 2, . . . , n}, represented geometrically as bargraphs, according to the number of 1 × 2 rectangles contained within the area subtended. In particular, we find both an explicit and an asymptotic formula for the total number of 1 × 2) rectangles taken over all partitions of [n].

Original languageEnglish
Pages (from-to)708-715
Number of pages8
JournalJournal of Difference Equations and Applications
Issue number5
StatePublished - 4 May 2019

Bibliographical note

Publisher Copyright:
© 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.


  • Bargraphs
  • generating functions
  • rectangle
  • set partitions

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics


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