I ran your Tartaglia project and tried some of the experiments. It is a very nice application with nice graphics. I know the triangle as Pascal's triangle and have used it for binomial expansion but I didn't know about (or I've forgotten some of) the other uses. Thanks for sharing this.

Your Perl code seems to be the same regex approach I used to eliminate duplicate digits. This by itself produces permutations. To get the 210 combinations add the split, sort and store in a hash.