COUNTING 1 \times 2 RECTANGLES IN SET PARTITIONS
Nenad Cakić, Toufik Mansour, Armend Sh · HAL (Le Centre pour la Communication Scientifique Directe) · 2018
In this paper, we study the generating function for the number of set partitions of [n] represented as bargraphs, according to the number of rectangles of dimensions 1 × 2. In particular, we find an explicit formula and an asymptotic formula for the total number of 1 × 2 rectangles over set partitions of [n].