The mathwords.com definition from bob would be a good dyadic definition for
perm. You can get there by taking all permutations of all combinations.
$3 comb 5
10 3
$perm 3
6 3
dyadicperm=: ,/@:(({~perm@#)"_1)@:comb
$3 dyadicperm 5
60 3
So comb is all (ordered) x-subsets of [y].
dyadicperm is all (with all orders) x-subsets of [y].
(These are only the same if x is 1).
I'm sure there is a better way to define it, but this is how perm should behave
if it were used dyadically.
-----Original Message-----
From: [email protected]
[mailto:[email protected]] 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
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Tirrell, Jordan
(Consultant)
Sent: Tuesday, June 26, 2012 3:07 PM
To: Programming forum
Subject: Re: [Jprogramming] permutation list
I don't think you'd ever want to use perm dyadically.
perm=. ! A.&i. ]
perm y gives all !y permutaions of y objects.
x perm y gives the first x!y permutations of y objects.
So dyadic perm is defined as the first x!y (or # x comb y) items of monadic
perm. I think this is simply a consequence of the intended monadic definition.
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Raul Miller
Sent: Tuesday, June 26, 2012 2:14 PM
To: Programming forum
Subject: Re: [Jprogramming] permutation list
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 <[email protected]> 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 <[email protected]> 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 <[email protected]> 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 <[email protected]> wrote:
>>>
>>>> 4 comb 10
>>>>
>>>>
>>>> R.E. Boss
>>>>
>>>>
>>>> > -----Oorspronkelijk bericht-----
>>>> > Van: [email protected] [mailto:
>>>> [email protected]] Namens ed bierly
>>>> > Verzonden: dinsdag 26 juni 2012 18:15
>>>> > Aan: [email protected]
>>>> > 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
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