# Moser Polynomials and Eulerian Numbers

## TL;DR

This paper explores properties of Moser polynomials, revealing their connections to Eulerian and Stirling numbers, and demonstrates their application in solving the multiset recovery problem.

## Contribution

It provides explicit formulas linking Moser polynomials with Eulerian and Stirling numbers and applies these to the multiset recovery problem.

## Key findings

- Derived explicit formulas connecting Moser polynomials with Eulerian and Stirling numbers.
- Showed how Moser polynomials can be used to solve the multiset recovery problem.
- Enhanced understanding of algebraic combinatorics through properties of Moser polynomials.

## Abstract

Article presents a short investigation into some properties of the Moser polynomials which appear in various problems from algebraic combinatorics. For instance, these polynomials can be used to solve the Generalized Moser's Problem on multiset recovery: Can a collection (multiset) of $n$ numbers can be uniquely restored given the collection of its $s$-sums? We prove some explicit formulas showing relationships between Moser polynomials and such popular algebraic combinatorial sequences as Eulerian and Stirling numbers.