Submultiplicative polynomials in combinatorics

Source abstract

Abstract For normalized sequences $$\left( g(n)\right) _{n\in \mathbb {N}}$$ g ( n ) n ∈ N we consider recursively defined polynomials $$P_n^g(x)$$ 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.