Set Partitions with Isolated Singletons
Augustine O. Munagi · American Mathematical Monthly · 2018
We give results for partitions of the set of the first n natural numbers into k nonempty subsets S1, S2, …, Sk with respect to the number of isolated elements, that is, with respect to integers a such that if a belongs to Si, then neither a − 1 nor a + 1 belongs to Si.