For large lists (where you don't have enough memory to store the entire array), I used to do this with the Combinatorica NthPermutation, now apparently UnrankPermutation. And it worked fine with lists composed of all different elements where I knew exactly how many permutations there were in total. That is not the case with the kind of lists with which I am now working: much larger versions of {-1,-1,-1,1,1,1} or {-1,-1,-1,0,1,1,1} to give examples for lengths 6 and 7. How many permutations are there and, more importantly, how do I step through them all, one at a time? An acquaintance who is working on the same problem in Sage was able to accomplish this simply by deleting .list() from the program line for p in Permutations(T).list():. Wow!