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Permutations Function

unknown

I've been looking through the JMP 8 manual for a function that returns every possible permutation of all the integers from 1 to N, but haven't been able to find one. I can write one easily enough, but I don't want to bother if there's one already available that I've overlooked. Is there one?

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mpb

Can the "col shuffle" function do what you need?

unknown

Unfortunately no: I need to look at every permutation systematically. As I said, I can write a function that will do it easily enough; I'm just a little surprised that there doesn't already appear to be one. I'd have thought that it would be a useful addition to the armoury.

Many thanks

You can achieve that with the "Cartesian Join" option in the Join platform. Create two tables with one column each and n rows. Join the second with the first table, and then rejoin the output with first n-1 times. I tried with n=3 and got a table with 27 rows containing every permutation (distributed over 3 columns).

Would be easy to script in a for loop (use invisible option for large n!), but that was maybe what you already had in mind.

unknown

Ingenious! But that's going to generate 27 (3x3x3) lists, i.e. {1, 1, 1}, {1, 1, 2}, {1, 1, 3}, {1, 2, 1}, ... , {3, 3, 3}, isn't it, whereas what I'd actually be after in such a situation would be just the following 6 (3x2x1) lists:

{1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2} and {3, 2, 1}

I could eliminate any of the lists generated from the cartesian join with duplicate integers easily enough, but there ought to be a more efficient way than that - maybe using a recursive function. If I think one up I'll post it unless anyone beats me to it.

Many thanks!