Depends on the text? But I don't think we have a full collection of partition routines to adequately address the various partitioning concepts ennumerated in the book linked from http://jsoftware.com/pipermail/programming/2017-October/049377.html
Thanks, -- Raul On Tue, Nov 7, 2017 at 7:43 AM, Erling Hellenäs <[email protected]> wrote: > Hi all! > > If we want to include parRuskeyE in a text about set partitions, we could > use this definition: > > SetPartitionsGenerateF =: 4 : 0 > NB. Generate all set partitions with k subsets from > NB. an original set with n unique items. > NB. x - number of subsets > NB. y - number of items in the set to partition > NB. Result - table of integers > NB. -each row is a generated set partition > NB. -columns contain the subset number of the items > NB. with the corresponding position in the set to > NB. partition. > NB. Algorithm from Frank Ruskey: Combinatorial Generation > NB. Working Version (1j-CSC 425/520). > (,: i.y) SPGF (x-1);y-1 > ) > > SPGF =: 4 : 0 > 'k n' =. y > r=. (0,_1{.$x)$0 > if. k=n do. > r=.x > else. > s=.n {."1 x > e=.(n+1)}."1 x > a=.,/s ( [,"1 1 (i.k+1),"0 1 ])"1 e > r=.r, a SPGF k;n-1 > if. k > 0 do. > a=.s,.k,.e > r=.r, a SPGF (k-1);n-1 > end. > end. > r > ) > > It could possibly be included in this page: > https://en.wikipedia.org/wiki/Partition_of_a_set > > I could include it with some minimal text. > > Opinions? > > Cheers, > > Erling Hellenäs > > > > Den 2017-11-07 kl. 11:50, skrev Erling Hellenäs: >> >> Hi all! >> >> I created a program for enumeration of multiset permutations. It could >> possibly be used to answer the Quora question. >> >> Comments are welcome. >> >> Display=: 4 : ' x { ~. y' >> >> N=: ,2 1 >> y=: ,6 6 7 >> MultisetPermutationsEnumerate N >> 0 0 1 >> 0 1 0 >> 1 0 0 >> (MultisetPermutationsEnumerate N )Display y >> 6 6 7 >> 6 7 6 >> 7 6 6 >> >> ------Project------------ >> >> MultisetPermutationsEnumerate =: 3 : 0 >> NB. Enumerate multiset or bag permutations. >> NB. y - vector with number of repetitions. >> NB. Result - table of permutations - indexes in the nub >> NB. of the multiset. >> NB. Algorithm from Frank Ruskey: Combinatorial Generation >> NB. Working Version (1j-CSC 425/520). >> p=.(+/y)#0 >> 'r p N'=. (p;y) MPERec <:#p >> |."1 r >> ) >> >> MPERec =: 4 : 0 >> 'p N'=.x >> if. (0{N) = >:y do. >> r=.,:p >> else. >> r=. (0,#p)$0 >> for_j. (N>0)#i.#N do. >> p=. j y } p >> N=. (<:j{N) j } N >> 't p N'=. (p;N) MPERec <:y >> r=.r,t >> N=. (>:j{N) j } N >> p=.0 y }p >> end. >> end. >> r;p;N >> ) >> >> Display=: 4 : ' x { ~. y' >> >> log=: ,.<i.0 >> N=: ,1 >> y=: ,6 >> MultisetPermutationsEnumerate N >> (MultisetPermutationsEnumerate N )Display y >> log=: ,.<i.0 >> N=: ,1 1 >> y=: ,6 7 >> MultisetPermutationsEnumerate N >> ( MultisetPermutationsEnumerate N )Display y >> N=: ,2 1 >> y=: ,6 6 7 >> MultisetPermutationsEnumerate N >> (MultisetPermutationsEnumerate N )Display y >> N=: ,2 1 1 >> y=: ,6 6 7 8 >> MultisetPermutationsEnumerate N >> (MultisetPermutationsEnumerate N )Display y >> N=: ,1 2 1 >> y=: ,7 6 6 8 >> MultisetPermutationsEnumerate N >> (MultisetPermutationsEnumerate N )Display y >> >> ---Output---- >> >> log=: ,.<i.0 >> N=: ,1 >> y=: ,6 >> MultisetPermutationsEnumerate N >> 0 >> (MultisetPermutationsEnumerate N )Display y >> 6 >> log=: ,.<i.0 >> N=: ,1 1 >> y=: ,6 7 >> MultisetPermutationsEnumerate N >> 0 1 >> 1 0 >> ( MultisetPermutationsEnumerate N )Display y >> 6 7 >> 7 6 >> N=: ,2 1 >> y=: ,6 6 7 >> MultisetPermutationsEnumerate N >> 0 0 1 >> 0 1 0 >> 1 0 0 >> (MultisetPermutationsEnumerate N )Display y >> 6 6 7 >> 6 7 6 >> 7 6 6 >> N=: ,2 1 1 >> y=: ,6 6 7 8 >> MultisetPermutationsEnumerate N >> 0 0 1 2 >> 0 0 2 1 >> 0 1 0 2 >> 0 1 2 0 >> 0 2 0 1 >> 0 2 1 0 >> 1 0 0 2 >> 1 0 2 0 >> 1 2 0 0 >> 2 0 0 1 >> 2 0 1 0 >> 2 1 0 0 >> (MultisetPermutationsEnumerate N )Display y >> 6 6 7 8 >> 6 6 8 7 >> 6 7 6 8 >> 6 7 8 6 >> 6 8 6 7 >> 6 8 7 6 >> 7 6 6 8 >> 7 6 8 6 >> 7 8 6 6 >> 8 6 6 7 >> 8 6 7 6 >> 8 7 6 6 >> N=: ,1 2 1 >> y=: ,7 6 6 8 >> MultisetPermutationsEnumerate N >> 0 1 1 2 >> 0 1 2 1 >> 0 2 1 1 >> 1 0 1 2 >> 1 0 2 1 >> 1 1 0 2 >> 1 1 2 0 >> 1 2 0 1 >> 1 2 1 0 >> 2 0 1 1 >> 2 1 0 1 >> 2 1 1 0 >> (MultisetPermutationsEnumerate N )Display y >> 7 6 6 8 >> 7 6 8 6 >> 7 8 6 6 >> 6 7 6 8 >> 6 7 8 6 >> 6 6 7 8 >> 6 6 8 7 >> 6 8 7 6 >> 6 8 6 7 >> 8 7 6 6 >> 8 6 7 6 >> 8 6 6 7 >> >> Cheers, >> >> Erling Hellenäs >> >> >> >> Den 2017-11-06 kl. 14:21, skrev Erling Hellenäs: >>> >>> Hi all! >>> >>> Do we have a program or built-in function to enumerate the permutations >>> of multisets, sets with item repetitions? >>> >>> Cheers, >>> >>> Erling Hellenäs >>> >>> >>> Den 2017-11-06 kl. 10:37, skrev Linda Alvord: >>>> >>>> This is handier when there are more sets of repetions. >>>> >>>> (!6)%(!2)*!2 >>>> 180 >>>> / >>>> (!6)%*/!2 2 >>>> 180 >>>> >>>> Linda >>>> >>>> -----Original Message----- >>>> From: Programming [mailto:[email protected]] On >>>> Behalf Of Erling Hellenäs >>>> Sent: Sunday, November 5, 2017 11:28 AM >>>> To: [email protected] >>>> Subject: Re: [Jprogramming] Partitions >>>> >>>> Hi all! >>>> >>>> Even though this solution is only relevant as an answer to the Quora >>>> question, I want to post a correction. >>>> Since there can be duplicates in the root sets, there is not always !n >>>> permutations. >>>> The formula is here: >>>> https://brilliant.org/wiki/permutations-with-repetition/ >>>> The corrected list: >>>> >>>> list=:4 : 0 >>>> v=.((x-1)#1),q: y >>>> r1=.x parRuskeyE #v >>>> r2=. >r1 (*/)@:{&.>"1 0 < v >>>> r3=./:~"1 r2 >>>> r4=. ~.r3 >>>> perm=.3 : '(!#y)%*/!+/y=/~.y' >>>> r5=.perm"1 r4 >>>> +/r5 >>>> ) >>>> >>>> Test output: >>>> >>>> v=: ((x-1)#1),q:u=:2*2*3*3 >>>> r1=:3 parRuskeyE #v >>>> r2=: >r1 (*/)@:{&.>"1 0 < v >>>> r3=:/:~"1 r2 >>>> [r4=: ~.r3 >>>> 1 2 18 >>>> 2 2 9 >>>> 1 4 9 >>>> 2 3 6 >>>> 3 3 4 >>>> 1 6 6 >>>> 1 3 12 >>>> 1 1 36 >>>> *./u =*/"1 r4 >>>> 1 >>>> perm=: 3 : '(!#y)%*/!+/y=/~.y' >>>> [r5=:perm"1 r4 >>>> 6 3 6 6 3 3 6 3 >>>> [+/r5 >>>> 36 >>>> >>>> 3 list 2*2*3*3 >>>> 36 >>>> >>>> perm 1 2 3 3 >>>> 12 >>>> (!4)%!2 >>>> 12 >>>> perm 1 2 3 3 5 5 >>>> 180 >>>> (!6)%(!2)*!2 >>>> 180 >>>> >>>> Cheers, >>>> >>>> Erling Hellenäs >>>> >>>> >>>> >>>> On 2017-11-03 18:24, Erling Hellenäs wrote: >>>>> >>>>> Hi all! >>>>> >>>>> list=:4 : 0 >>>>> v=.((x-1)#1),q: y >>>>> r1=.x parRuskeyE #v >>>>> r2=. >r1 (*/)@:{&.>"1 0 < v >>>>> r3=./:~"1 r2 >>>>> r4=. ~.r3 >>>>> (!x)*#r4 >>>>> ) >>>>> >>>>> 3 list 24 >>>>> 36 >>>>> >>>>> Cheers, >>>>> Erling Hellenäs >>>>> >>>>> On 2017-11-03 17:36, Erling Hellenäs wrote: >>>>>> >>>>>> Hi all ! >>>>>> >>>>>> Below is the output of the run on the Quora question. >>>>>> >>>>>> Maybe someone can see if there is a problem. >>>>>> >>>>>> Cheers, >>>>>> >>>>>> Erling Hellenäs >>>>>> >>>>>> [v=: 1 1 ,q:24 >>>>>> 1 1 2 2 2 3 >>>>>> [r=:3 parRuskeyE #v >>>>>> ┌───────┬───────┬───────┐ >>>>>> │0 3 4 5│1 │2 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 4 5 │1 3 │2 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 4 5 │1 │2 3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 5 │1 4 │2 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 5 │1 3 4 │2 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 5 │1 4 │2 3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 5 │1 │2 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 5 │1 3 │2 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 5 │1 │2 3 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 4 │1 5 │2 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 4 │1 3 5 │2 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 4 │1 5 │2 3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 │1 4 5 │2 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 3 4 5│2 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 4 5 │2 3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 │1 5 │2 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 3 5 │2 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 5 │2 3 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 4 │1 │2 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 4 │1 3 │2 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 4 │1 │2 3 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 │1 4 │2 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 3 4 │2 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 4 │2 3 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 │1 │2 4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 3 │2 4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 │2 3 4 5│ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 4 5│1 │3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 4 5 │1 2 │3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 5 │1 4 │3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 5 │1 2 4 │3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 5 │1 │3 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 5 │1 2 │3 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 4 │1 5 │3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 4 │1 2 5 │3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 │1 4 5 │3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 2 4 5│3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 │1 5 │3 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 2 5 │3 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 4 │1 │3 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 4 │1 2 │3 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 │1 4 │3 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 2 4 │3 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 │1 │3 4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 2 │3 4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 4 5│2 │3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 5 │2 4 │3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 5 │2 │3 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 4 │2 5 │3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 │2 4 5 │3 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 │2 5 │3 4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 4 │2 │3 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 │2 4 │3 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 │2 │3 4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 3 5│1 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 5 │1 2 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 5 │1 3 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 5 │1 2 3 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 3 │1 5 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 │1 2 5 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 │1 3 5 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 2 3 5│4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 3 │1 │4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 │1 2 │4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 │1 3 │4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 2 3 │4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 3 5│2 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 5 │2 3 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 3 │2 5 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 │2 3 5 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 3 │2 │4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 │2 3 │4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 2 5│3 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 2 │3 5 │4 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 2 │3 │4 5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 3 4│1 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 4 │1 2 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 4 │1 3 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 4 │1 2 3 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 3 │1 4 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 3 │1 2 4 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 2 │1 3 4 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 │1 2 3 4│5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 3 4│2 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 4 │2 3 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 3 │2 4 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 │2 3 4 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 2 4│3 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 2 │3 4 │5 │ >>>>>> ├───────┼───────┼───────┤ >>>>>> │0 1 2 3│4 │5 │ >>>>>> └───────┴───────┴───────┘ >>>>>> [r2=: >r (*/)@:{&.>"1 0 < v >>>>>> 12 1 2 >>>>>> 6 2 2 >>>>>> 6 1 4 >>>>>> 6 2 2 >>>>>> 3 4 2 >>>>>> 3 2 4 >>>>>> 6 1 4 >>>>>> 3 2 4 >>>>>> 3 1 8 >>>>>> 4 3 2 >>>>>> 2 6 2 >>>>>> 2 3 4 >>>>>> 2 6 2 >>>>>> 1 12 2 >>>>>> 1 6 4 >>>>>> 2 3 4 >>>>>> 1 6 4 >>>>>> 1 3 8 >>>>>> 4 1 6 >>>>>> 2 2 6 >>>>>> 2 1 12 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 1 2 12 >>>>>> 2 1 12 >>>>>> 1 2 12 >>>>>> 1 1 24 >>>>>> 12 1 2 >>>>>> 6 2 2 >>>>>> 6 2 2 >>>>>> 3 4 2 >>>>>> 6 1 4 >>>>>> 3 2 4 >>>>>> 4 3 2 >>>>>> 2 6 2 >>>>>> 2 6 2 >>>>>> 1 12 2 >>>>>> 2 3 4 >>>>>> 1 6 4 >>>>>> 4 1 6 >>>>>> 2 2 6 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 2 1 12 >>>>>> 1 2 12 >>>>>> 6 2 2 >>>>>> 3 4 2 >>>>>> 3 2 4 >>>>>> 2 6 2 >>>>>> 1 12 2 >>>>>> 1 6 4 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 1 2 12 >>>>>> 12 1 2 >>>>>> 6 2 2 >>>>>> 6 2 2 >>>>>> 3 4 2 >>>>>> 4 3 2 >>>>>> 2 6 2 >>>>>> 2 6 2 >>>>>> 1 12 2 >>>>>> 4 1 6 >>>>>> 2 2 6 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 6 2 2 >>>>>> 3 4 2 >>>>>> 2 6 2 >>>>>> 1 12 2 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 6 2 2 >>>>>> 2 6 2 >>>>>> 2 2 6 >>>>>> 8 1 3 >>>>>> 4 2 3 >>>>>> 4 2 3 >>>>>> 2 4 3 >>>>>> 4 2 3 >>>>>> 2 4 3 >>>>>> 2 4 3 >>>>>> 1 8 3 >>>>>> 4 2 3 >>>>>> 2 4 3 >>>>>> 2 4 3 >>>>>> 1 8 3 >>>>>> 4 2 3 >>>>>> 2 4 3 >>>>>> 4 2 3 >>>>>> [r3=:/:~"1 r2 >>>>>> 1 2 12 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 2 2 6 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 1 4 6 >>>>>> 2 3 4 >>>>>> 1 3 8 >>>>>> 2 3 4 >>>>>> 2 2 6 >>>>>> 2 3 4 >>>>>> 2 2 6 >>>>>> 1 2 12 >>>>>> 1 4 6 >>>>>> 2 3 4 >>>>>> 1 4 6 >>>>>> 1 3 8 >>>>>> 1 4 6 >>>>>> 2 2 6 >>>>>> 1 2 12 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 1 2 12 >>>>>> 1 2 12 >>>>>> 1 2 12 >>>>>> 1 1 24 >>>>>> 1 2 12 >>>>>> 2 2 6 >>>>>> 2 2 6 >>>>>> 2 3 4 >>>>>> 1 4 6 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 2 2 6 >>>>>> 2 2 6 >>>>>> 1 2 12 >>>>>> 2 3 4 >>>>>> 1 4 6 >>>>>> 1 4 6 >>>>>> 2 2 6 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 1 2 12 >>>>>> 1 2 12 >>>>>> 2 2 6 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 2 2 6 >>>>>> 1 2 12 >>>>>> 1 4 6 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 1 2 12 >>>>>> 1 2 12 >>>>>> 2 2 6 >>>>>> 2 2 6 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 2 2 6 >>>>>> 2 2 6 >>>>>> 1 2 12 >>>>>> 1 4 6 >>>>>> 2 2 6 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 2 2 6 >>>>>> 2 3 4 >>>>>> 2 2 6 >>>>>> 1 2 12 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 2 2 6 >>>>>> 2 2 6 >>>>>> 2 2 6 >>>>>> 1 3 8 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 1 3 8 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 1 3 8 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> 2 3 4 >>>>>> [r4=: ~.r3 >>>>>> 1 2 12 >>>>>> 2 2 6 >>>>>> 1 4 6 >>>>>> 2 3 4 >>>>>> 1 3 8 >>>>>> 1 1 24 >>>>>> *./24 =*/"1 r4 >>>>>> 1 >>>>>> NB. All permutations >>>>>> (!3)*#r5 >>>>>> 312 >>>>>> --------------------------------------------------------------------- >>>>>> - 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
