Submultiplicative Polynomials in Combinatorics

Abstract

For normalized sequences ${\left(g(n)\right)}_{n\in \mathbb{N}}$ we consider recursively defined polynomials $P_n^g(x)$. In this paper we study their submultiplicative property, viewed as a Bessenrodt--Ono type inequality for the partition function, and provide an effective criterion for establishing it.

11 pages