Its relative to the sorted order of the input
rp1 =: (] (] <@; $:^:(1<#)@del1~)"1 0 ~.@])
untreep =: (({.,"0 1 $:^:(1<L.)@}.)&>)
rperm6 =: (a: ;"1@(]#~ -.@e."1) ,&.:(<"1)@:untreep@:rp1)
rperm6 0 0 1
0 0 1
0 1 0
1 0 0
rperm6 0 1 1
0 1 1
1 0 1
1 1 0
in both cases, the 0 index is the sorted order
permN 1 0 1
1
permN 1 0 0
2
the index in their respective permutation lists.
----- Original Message -----
From: Raul Miller <[email protected]>
To: Programming forum <[email protected]>
Sent: Thursday, May 5, 2016 6:13 PM
Subject: Re: [Jprogramming] permutation and combination numbers (with repeat)
Why are these two results equal?
permN 0 0 1
0
permN 0 1 1
0
Thanks,
--
Raul
On Thu, May 5, 2016 at 5:58 PM, 'Pascal Jasmin' via Programming
<[email protected]> wrote:
> Some routines to calculate permutation and combination numbers, similar to A.
> (but allows permutations with repeat)
>
> del1 =: i.~ ({. , >:@[ }. ]) ]
>
> combN =: (0:`((<:@[ - {.@]) $: >:@{.@] -~ }.@])@.(0 < #@]) + 0:`(<:@#@] +/@:!
> <:@[ - i.@{.@])@.(0 < {.@]) )
>
> combNF =: 3 : 'a =. 1 { 0 {:: y label_. (i.a) + +/\ 1 {:: ([ (] ;~ [ - 1 ,~
> _2 >:@{ ]) }:@] , {:@] ([ ({.@] ,(- {:)) ] (] , {~) 1 i:~ >:) (0 , ] (+/\)@:!
> ( a i.@:-~ [) -~ [)/@:<:@[ )&>/^: (<:a) y'@:;
>
> permC =: # %&(x:@:(*/))&:! #/.~
>
> permN1 =: ((0:`( (] - <./)@:({.@] del1 [) $: (] - <./)@:}.@] )@.(1 < #@])) +
> (permC % #)@] * [ i. {.@] ) f.
>
> permN =: /:~ permN1 ]
>
> 100x combN 15 25 35 45 55 65 85
> 11284989655
>
> 100 7 combNF 11284989655x
> 15 25 35 45 55 65 85
>
> permN 1 0 0 2 1 3 3 1
> 434
>
> haven't done the reverse to permN yet, but these routines combined can be
> used to compress any list into 2 numbers (with a key). You can google for
> combinatorial number base, and there is A., but not sure A. has been done for
> permutations with repeats. Which produces smaller numbers than A. does (due
> to fewer underlying permutations).
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