On the powers of the descent set statistic

TL;DR

This paper investigates the behavior of the sum of the r-th powers of the descent set statistic, focusing on its prime factorization and how it relates to the base p expansion of n and r.

Contribution

It provides new insights into the prime factorization of sums of powers of the descent set statistic based on base p expansions.

Findings

The sum's prime factors are influenced by the base p expansion of n and r.

The paper establishes relationships between the descent set statistic powers and prime factors.

Results depend on the base p expansion, revealing structural properties of these sums.

Abstract

We study the sum of the $r$th powers of the descent set statistic and how many small prime factors occur in these numbers. Our results depend upon the base $p$ expansion of $n$ and $r$.