Take the time to ponder R. E. Boss's version (in the Wiki). It is
beautiful, and I have tried without success to make any improvement.
$ 12 comb 24
2704156 12
In about 1 second.
Henry Rich
On 6/26/2012 8:54 PM, Linda Alvord wrote:
> 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-boun...@jsoftware.com
> [mailto:programming-boun...@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<devon...@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<rauldmil...@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<ebie...@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.b...@planet.nl> wrote:
>>>>>
>>>>>> 4 comb 10
>>>>>>
>>>>>>
>>>>>> R.E. Boss
>>>>>>
>>>>>>
>>>>>>> -----Oorspronkelijk bericht-----
>>>>>>> Van: programming-boun...@jsoftware.com [mailto:
>>>>>> programming-boun...@jsoftware.com] Namens ed bierly
>>>>>>> Verzonden: dinsdag 26 juni 2012 18:15
>>>>>>> Aan: programming@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
>>>>>> http://www.jsoftware.com/forums.htm
>>>>>>
>>>>> -------------------------------------------------------------------
>>>>> --- For information about J forums see
>>>>> http://www.jsoftware.com/forums.htm
>>>> --------------------------------------------------------------------
>>>> -- For information about J forums see
>>>> http://www.jsoftware.com/forums.htm
>>>
>>>
>>>
>>> --
>>> Devon McCormick, CFA
>>> ^me^ at acm.
>>> org is my
>>> preferred e-mail
>>> ---------------------------------------------------------------------
>>> - For information about J forums see
>>> http://www.jsoftware.com/forums.htm
>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
> ----------------------------------------------------------------------
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>
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