$: here means the same thing that pn means (and it would have been
clearer if pn had been used instead of $:

If $: had just been the left verb in the gerund, you would be getting
a domain error from trying to use i. on a complex argument (rec's
arguments would go negative and we put them through %: on the way into
i.)

-- 
Raul

On Thu, Jul 26, 2012 at 12:16 PM, David Vaughan <[email protected]> wrote:
> I was looking through the essay on the wiki about partitions, and I was 
> looking at the verb pn:
>
> pn =: -/@(+/)@:($:"0)@rec ` (x:@(0&=)) @. (0>:]) M.
> rec =: - (-: (*"1) _1 1 +/ 3 * ]) @ (>:@i.@>.@%:@((2%3)&*))
>
> I was a little confused about the way that $: works - does it re-execute the 
> whole verb pn or just the first train of that tie?
>
> Thanks.
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