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    <p>I noticed that your updated getPerms function contains duplicates. Here's my crack at a dupe-free version. Hopefully the comments speak for themselves. The hardest part was writing an efficient <code>distrib</code> function, because the concatenation operator has to be used somewhere. Luckily it's only used on small sublists, so the performance remains reasonable. My getAllPerms code below generates all permutations of [1..9] in around a quarter of a second, all 10-element permutations in around 2.5 seconds.</p> <p><em>Edit: funny, I didn't look at Tomas' code, but his combinations function and my picks function are nearly identical.</em></p> <pre><code>// All ordered picks {x_i1, x_i2, .. , x_ik} of k out of n elements {x_1,..,x_n} // where i1 &lt; i2 &lt; .. &lt; ik let picks n L = let rec aux nleft acc L = seq { match nleft,L with | 0,_ -&gt; yield acc | _,[] -&gt; () | nleft,h::t -&gt; yield! aux (nleft-1) (h::acc) t yield! aux nleft acc t } aux n [] L // Distribute an element y over a list: // {x1,..,xn} --&gt; {y,x1,..,xn}, {x1,y,x2,..,xn}, .. , {x1,..,xn,y} let distrib y L = let rec aux pre post = seq { match post with | [] -&gt; yield (L @ [y]) | h::t -&gt; yield (pre @ y::post) yield! aux (pre @ [h]) t } aux [] L // All permutations of a single list = the head of a list distributed // over all permutations of its tail let rec getAllPerms = function | [] -&gt; Seq.singleton [] | h::t -&gt; getAllPerms t |&gt; Seq.collect (distrib h) // All k-element permutations out of n elements = // all permutations of all ordered picks of length k combined let getPerms2 n lst = picks n lst |&gt; Seq.collect getAllPerms </code></pre> <p><em>Edit: more code in response to comments</em></p> <pre><code>// Generates the cartesian outer product of a list of sequences LL let rec outerProduct = function | [] -&gt; Seq.singleton [] | L::Ls -&gt; L |&gt; Seq.collect (fun x -&gt; outerProduct Ls |&gt; Seq.map (fun L -&gt; x::L)) // Generates all n-element combination from a list L let getPermsWithRep2 n L = List.replicate n L |&gt; outerProduct </code></pre>
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    1. POCombinations and Permutations in F#
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    1. COThanks for that; it does indeed run a good bit quicker than mine! (My code in the edit works properly, with a very small change, but still slower.) I'm wondering if your distribute function is really equivalent to my rotations one...
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    2. COIf you can show me how to do permutations *with* repetitions too, that would be great!
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    3. CO@Noldorin: the distribute and rotate functions do something different, but the result in generating permutations is equivalent. You take a list and rotate it n times and stick the rotated heads to the permutations of the tails. I take the head of a list and distribute it over the permutations of the tail. The permutations are the same, but the algorithms output them in a different order. Regarding your second question, the output of your getPermsWithRep function looks like the outer product of n copies of L. I've edited my answer to include this.
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