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For any set $S$, $\mathcal{P}(S)$ denotes the power set of $S$ and $\emptyset \in \mathcal{P}(S)$ always holds. Essentially, I want to denote the set that equals the power set (of some $S$) but excluding the empty set. I was thinking about writing $\mathcal{P}^+$ and defining that (as $\mathcal{P}^+(S) := \mathcal{P}(S) - \emptyset = \mathcal{P}(S)\setminus \{\emptyset\}$), but this could be a common enough thing that someone already established a notation for it.

Wikipedia et al. don't mention anything, but maybe there is something nevertheless. I would prefer to use an established notation if there is one (while still defining what I mean).

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    I don’t know of any standard notation. The only notation that I’ve seen more than once (that I can recall) is $\wp^*(S)$.2012-10-26

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