A clean tacit version of (n choose k) in J Listing all \$\binom{n}{k}\$ combinations of i is a well-solved problem in J. From that article, there is this implementation:


comb=: 4 : 0
 k=. i.&gt;:d=.y-x
 z=. (d$&lt;i.0 0),&lt;i.1 0
 for. i.x do. z=. k ,.&amp;.&gt; ,&amp;.&gt;/\. &gt;:&amp;.&gt; z end.
 ; z
)



used as follows:

   4 comb 6
0 1 2 3
0 1 2 4
0 1 2 5
0 1 3 4
0 1 3 5
0 1 4 5
0 2 3 4
0 2 3 5
0 2 4 5
0 3 4 5
1 2 3 4
1 2 3 5
1 2 4 5
1 3 4 5
2 3 4 5


I am interested primarily in clean, tacit version. Here's what I have so far:

comb=. ~.@:(/:~"1)@(i.@[ {"1 (i.@! A. i.)@])


but that feels overly complex and verbose. Is there a better tacit implementation?
Your initial verb is a good start. Your code could be shortened to 24 bytes

~.@(/:~@:{"1~i.)~!A.&amp;i.]


A shorter version for 22 bytes can be found by permuting the binary string with k 1's.

[:I.@~.i.@!@]A.]{.1#~[


These are both O(n!) for C(n, k).