This does not answer your question, and it's not even a Perl suggestion, but I have to ask ...

why use permutations *at all*?

If the only requirement is to allow a user-definable ordering of known table fields, why not just give the user four 'select' boxes, one for each column?

In other words, give the user four of these ... one for each 'column'. (Line them up left to right so it is intuitive).

{select}
   {fname}
   {lname}
   {title}
   {phone}
   {_leave_blank_}
{/select}
[download]

This is not an 'elegant' solution, but does not seem any worse than giving the user a list of *every possible permutation of the ordering*, (including orderings where zero or more columns are excluded)! The least kludgy solution is to use a GUI control that is intended for this specific purpose. Mozilla Firebird has one. Just something to think about.