Moser Polynomials and Eulerian Numbers

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.