Residue class biases in unrestricted partitions, partitions into distinct parts, and overpartitions

We prove specific biases in the number of occurrences of parts belonging to two different residue classes a and b, modulo a fixed non-negative integer m, for the sets of unrestricted partitions, partitions into distinct parts, and overpartitions. These biases follow from inequalities for residue-weighted partition functions for the respective sets of partitions. We also establish asymptotic formulas for the numbers of partitions of size n that belong to these sets of partitions and have a symmetric residue bias (i.e., for 1≤ a<m/2 and $b=m-a$), as n tends to infinity.