I have a set $S = \{1,2,\ldots,n\}$ of $n$ elements and I denote with $P(S)$ the powerset of $S$.
Which is a correct and accepted notation to say that the set $Z$ is composed by all the elements in $P(S)$ with the exception of all the subsets of cardinality $h$?
Example: if $S=\{1,2,3\}$ then $P(S) = \{\emptyset, \{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\}$.
If $h = 1$, then it should be $Z = \{\emptyset, \{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\}=P(S)\setminus\{\{1\},\{2\},\{3\}\}$.
How can it be expressed in a formal and concise way, for any value of $n$ and $h$?
Thanks