Jan, I know what you mean but I doubt that you are right.

The sample data you gave us so far is not sufficient to determine a strict order of all elements.

(update e.g for the data given in Re^3: Converting Arrays into Matrix it's impossible to tell if A or 3 is the first element.)

And it doesn't make much sense that someone else ordered different subsets in such a way without you already knowing that order.

Anyway if you're theory is true, there is a pretty straight forward way to calculate this order.

Check the first element of all sets, if exactly one of them never appears in a higher position you found your alpha-element.

Now delete alpha from all sets and start again investigating the first elements to detect your beta.

At the end you either have a strict order in an array @ordered or you've found at least one case of ambiguity of your data.

Then put @ordered into my algorithm instead of sort keys ... and you've got your matrix.