maybe this is a cogent arg to hide(byte code)Boss's implementation in a primitive(verb)?
On Tue, Jun 26, 2012 at 9:32 PM, Linda Alvord <lindaalv...@verizon.net>wrote: > My version made it to 12!22 but very slowly. > > The original request in this thread was for code which did not include > looping, so I thought my version might be interesting. > > $12 comb 22 > 12 646646 > > Linda > > -----Original Message----- > From: programming-boun...@jsoftware.com > [mailto:programming-boun...@jsoftware.com] On Behalf Of Henry Rich > Sent: Tuesday, June 26, 2012 9:17 PM > To: Programming forum > Subject: Re: [Jprogramming] permutation list > > 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 > > > > ---------------------------------------------------------------------- > > 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
