  Unrefinable partitions are a subset of partitions into distinct parts which
satisfy an additional unrefinability property. More precisely, being an
unrefinable partition means that none of the parts can be written as the sum of
smaller integers without introducing a repetition. We address the algorithmic
aspects of unrefinable partitions, such as testing whether a given partition is
unrefinable or not and enumerating all the partitions whose sum is a given
integer. We design two algorithms to solve the two mentioned problems and we
discuss their complexity.
