Partition identities II. The results of Bateman and Erdős Original Research Article

This paper shows that the natural setting for the Bateman and Erdős study of monotonicity of the kth difference of partition functions a(n) is the class of partition identitiesimagewith polynomially bounded p(n). The results include a proof of their conjecture generalized to polynomially bounded p(n)—their conjecture was for p(n)set membership, variant{0,1}.