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].
Original language | American English |
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Pages (from-to) | 708-715 |
Number of pages | 8 |
Journal | Journal of Difference Equations and Applications |
Volume | 25 |
Issue number | 5 |
DOIs | |
State | Published - 4 May 2019 |
Keywords
- Bargraphs
- generating functions
- rectangle
- set partitions
All Science Journal Classification (ASJC) codes
- Analysis
- Algebra and Number Theory
- Applied Mathematics