Definition:Set Partition/Definition 2

Definition
Let $S$ be a set.

A partition of $S$ is a set of non-empty subsets $\Bbb S$ of $S$ such that each element of $S$ lies in exactly one element of $\Bbb S$.

Also defined as
Some sources do not impose the condition that all sets in $\Bbb S$ are non-empty.

This is most probably more likely to be an accidental omission rather than a deliberate attempt to allow $\varnothing$ to be an element of a partition.

The point is minor; proofs of partitionhood usually include a demostration that all elements of such a partition are indeed non-empty.

Also see

 * Equivalence of Definitions of Partition of Sets