User blog comment:DrCeasium/Hyperfactorial array notation: Analysis part 3/@comment-5529393-20130530121945/@comment-5529393-20130530145116

Basically, yes. A key feature is that there are different cardinal levels, and doing the same thing at a higher cardinal level will have a much greater effect when you collapse on down. I don't see how your notation can duplicate that unless it has different "levels" of its own, and your k-brackets don't qualify.