[Jprogramming] permutation list

[Linda Alvord]

I wrote a book called "Probability in APL" many years ago.  When I started
to learn J I tried to rewrite my code in J.  Here is what I wrote for
combinations.

   po=: [: |: ] #: [: i. */            
   cr=:[: |: ([ = [: +/ [: po ] $ 2:) #"1 [: po ] $ 2:
   comb=:[: |: (! , [) $ ([: , cr) #"1 [: , ([: $ cr) $ [: i. ]
   $4 comb 10
4 210
   
It might take a little time to remember what I did.

Linda 


-----Original Message-----
From: programming-bounces at jsoftware.com
[mailto:programming-bounces at jsoftware.com] On Behalf Of bob therriault
Sent: Tuesday, June 26, 2012 3:02 PM
To: Programming forum
Subject: Re: [Jprogramming] permutation list

Raul,

I don't think that there is a 1-1 correspondence between combinations and
permutations, since each combination of items can have a number of different
permutations. In the example you give the number of items is the same
because the difference in the two arguments is 1, but this would not be true
in the general case.

I am using the definition of combination found here:
http://www.mathwords.com/c/combination_formula.htm
and the formula for permutation found here:
http://www.mathwords.com/p/permutation_formula.htm

In J the number of combinations is x!y and the number of permutations is
x(!@-~ * !)y, since there are !(y-x) permutations of each combination. I
guess that this would make the correspondence !(y-x) to 1.

It's been a while since I sat in a combinatorics lecture, so please correct
me if I have this wrong, or I am using the words in a different way than
you.

Cheers, bob

On 2012-06-26, at 11:14 AM, Raul Miller wrote:

> They are certainly different.
> 
>   2 comb 3
> 0 1
> 0 2
> 1 2
>   2 perm 3
> 0 1 2
> 0 2 1
> 1 0 2
> 
> 
> In general, for n of m permutations and n of m combinations, the 
> permutations are going to be longer (length m instead of length n).
> But the number of distinct items will be the same.
> 
> --
> Raul
> 
> On Tue, Jun 26, 2012 at 2:09 PM, Devon McCormick <devonmcc at gmail.com>
wrote:
>> I thought that in the usual mathematical definition, combinations and 
>> permutations differ: for permutations, order matters; for 
>> combinations, it does not.  Under this definition, the combinations 
>> of
>> 3 things is just " i. 3 " - assuming we don't allow replacement?  If 
>> we do allow replacement, the permutations of 3 things are given by "
>> {3$<i.3 " and the combinations by something like " ~./:~&.>,{3$<i.3 ".
>> 
>> Does this seem right?
>> 
>> On Tue, Jun 26, 2012 at 12:51 PM, Raul Miller <rauldmiller at gmail.com>
wrote:
>>> Note that the number of combinations and the number of permutions are
the same.
>>> 
>>> And, perm is just: ! A.&i. ]
>>> 
>>> It seems like there ought to be a way of putting the permutations in 
>>> 1 to 1 correspondence with the combinations (to give us a concise 
>>> expression for combinations).
>>> 
>>> --
>>> Raul
>>> 
>>> On Tue, Jun 26, 2012 at 12:41 PM, ed bierly <ebierly at gmail.com> wrote:
>>>> yes combinations not permutations
>>>> thought there might be a way that didn't loop thank you for the 
>>>> references
>>>> 
>>>> On Tue, Jun 26, 2012 at 12:30 PM, R.E. Boss <r.e.boss at planet.nl> wrote:
>>>> 
>>>>> 4 comb 10
>>>>> 
>>>>> 
>>>>> R.E. Boss
>>>>> 
>>>>> 
>>>>>> -----Oorspronkelijk bericht-----
>>>>>> Van: programming-bounces at jsoftware.com [mailto:
>>>>> programming-bounces at jsoftware.com] Namens ed bierly
>>>>>> Verzonden: dinsdag 26 juni 2012 18:15
>>>>>> Aan: programming at jsoftware.com
>>>>>> Onderwerp: [Jprogramming] permutation list
>>>>>> 
>>>>>> what is the best way to get this list of 210 vectors?
>>>>>> 
>>>>>> 4!10
>>>>>> -----------------------------------------------------------------
>>>>>> ----- For information about J forums see 
>>>>>> http://www.jsoftware.com/forums.htm
>>>>> 
>>>>> ------------------------------------------------------------------
>>>>> ---- For information about J forums see 
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>>>>> 
>>>> -------------------------------------------------------------------
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>>> --------------------------------------------------------------------
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>> 
>> 
>> 
>> --
>> Devon McCormick, CFA
>> ^me^ at acm.
>> org is my
>> preferred e-mail
>> ---------------------------------------------------------------------
>> - For information about J forums see 
>> http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
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