I have been looking at algorithms that allow you to generate $k$-combinations of a given string.
My question is that why isn't the algorithm used to generate power sets used to generate the combinations of a given string? That is, we can just use a binary counter of length $n$ with $k$ ones set to select $k$ elements from a length $n$ string. The method is very simple.
I mean, the power set can represent all $k$-combinations of the input. So why use complex algorithms like the ones described here (e.g., Gray codes)?