Submultiplicative polynomials in combinatorics

For normalized sequences ( g(n)) n∈ N g ( n ) n ∈ N we consider recursively defined polynomials Pₙᵍ(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.