  Partitions with even (respectively odd) parts distinct and all other parts
unrestricted are often referred to as PED (respectively POD) partitions. In
this article, we generalize these notions and study sets of partitions in which
parts with fixed residue(s) modulo r are distinct while all other parts are
unrestricted. We also study partitions in which parts divisible by r
(respectively congruent to r modulo 2r) must occur with multiplicity greater
than one.
