Counting 1 × 2 rectangles in set partitions. Issue 5 (4th May 2019)

• Record Type: Journal Article
• Authors: Cakić, Nenad; Mansour, Toufik; Shabani, Armend Sh.
• Is Part Of: Journal of difference equations and applications. Volume 25:Issue 5(2019)
• Page Start: 708
• Page End: 715
• Publication Date: 2019-05-04
• Subjects: Bargraphs -- generating functions -- 1×2 rectangle -- set partitions; 05A18; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2019.1619712
• Languages: English
• ISSNs: 1023-6198

Abstract

ABSTRACT: 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 ] .