A probabilistic proof of a recurrence relation for sums of values of degenerate falling factorials

TL;DR

This paper provides a probabilistic proof for a recurrence relation involving sums of degenerate falling factorials, extending recent probabilistic methods to this degenerate case.

Contribution

It introduces a novel probabilistic approach to establish a recurrence relation for sums of degenerate falling factorials, expanding the scope of probabilistic proofs in combinatorics.

Findings

Established a recurrence relation for sums of degenerate falling factorials.

Provided a probabilistic proof technique for these sums.

Extended probabilistic methods to degenerate factorial functions.

Abstract

In this paper, we consider sums of values of degenerate falling factorials and give a probabilistic proof of a recurrence relation for them. This may be viewed as a degenerate version of the recent probabilistic proofs on sums of powers of integers.