Elements protected by records in set partitions

ABSTRACT

In this paper, we study the generating functions for the number of set partitions of $\left[n\right]$ according to the number/sum of elements protected by weak/strong records (smaller elements that follow the weak/strong records). In particular, we present explicit formulas and asymptotics for the total number of number/sum of elements protected by weak/strong records over set partitions of $\left[n\right]$.

KEYWORDS:

• Set partitions
• records
• protected by strong records
• protected by weak records

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 05A18
• 05A15
• 05A16