# Height of records in partitions of a set

## TL;DR

This paper investigates the properties of strong and weak records in set partitions, providing exact formulas for their counts and heights, advancing combinatorial understanding of partition structures.

## Contribution

It introduces new exact formulas for counting strong and weak records in set partitions, extending previous combinatorial results.

## Key findings

- Exact formulas for the number of strong records with height one
- Total sum of record heights over set partitions
- Number of partitions with a specified maximal height of strong records

## Abstract

We study the restricted growth function associated with set partitions, and obtain exact formulas for the number of strong records with height one, the total of record heights over set of partitions, and the number of partitions with a given maximal height of strong records. We also extend some of these results to weak records.