Martin: start collecting the answers
Michal: fix k-admissibility definition; [n] and other fixes

- I changed the definition of k-admissibility as we didn't have a correct one.
This lead one of the reviewers to bail out.
Now hopefully everything we say is correct but we should double-check.

- I did some small edits here and there.

- I changed [n] notation to {1,...,n} notation as
one of the reviewers complained about it.