# What does [n] mean here?

What is the meaning of $[n]$ ? Is it power set of $\{1,2,3...n\}$?

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No, it's just the set $\{ 1,2,\dots,n \}$. If you look at the notation carefully, you see that $S$ is written a subset of that set; if they meant the powerset they would have written $S$ as an element of the powerset.
It's probably the set $\{ 1,2,\ldots,n\}$.