I don't know how the semicolons are placed, but this code formats Raul's
output to give the shape you showed with only commas.
comb =. ,.(</.~ {.@{.@>) (</.~ /:~"1)1+5 5 5 #: i. 5^3
comb =. ((,~ #&(<,:4#' '))&.> i.@#) (',',.~{.@":"0)L:0 comb
; ,&LF&.> <@({.~i:&',')"1 ; ,.&:>/@:({.&.>~ [:>./#@>)&.> comb
111,112,113,114,115,122,123,124,125,133,134,135,144,145,155
121,131,141,151,212,132,142,152,313,143,153,414,154,515
211,311,411,511,221,213,214,215,331,314,315,441,415,551
231,241,251, 341,351, 451
312,412,512, 413,513, 514
321,421,521, 431,531, 541
222,223,224,225,233,234,235,244,245,255
232,242,252,323,243,253,424,254,525
322,422,522,332,324,325,442,425,552
342,352, 452
423,523, 524
432,532, 542
333,334,335,344,345,355
343,353,434,354,535
433,533,443,435,553
453
534
543
444,445,455
454,545
544,554
555
Marshall
On Thu, Aug 08, 2013 at 03:34:32PM -0400, Raul Miller wrote:
> If I ignore formatting issues, this gives the basic structure:
>
> ,.(</.~ {.@{.@>) (</.~ /:~"1)1+5 5 5 #: i. 5^3
>
> FYI,
>
> --
> Raul
>
> On Thu, Aug 8, 2013 at 3:29 PM, Atto Ampere <[email protected]> wrote:
> > I came across this chart in an 200 year old publication..
> > and was wasting my time figuring out by hand the laws by which it is
> > governed just because i couldn't use J, which seems a perfect fit for
> > it!
> >
> >
> >
> > 111,112,113,114,115;122,123,124,125;133,134,135;144,145;155
> > 121,131,141,151;212,132,142,152;313,143,153;414,154;515
> > 211,311,411,511;221,213,214,215;331,314,315;441,415;551
> > 231,241,251; 341,351; 451;
> > 312,412,512; 413,513; 514;
> > 321,421,521; 431,531; 541;
> > 222,223,224,225;233,234,235;244,245;255
> > 232,242,252;323,243,253;424,254;525
> > 322,422,522;332,324,325;442,425;552
> > 342,352; 452;
> > 423,523; 524;
> > 432,532; 542;
> > 333,334,335;344,345;355
> > 343,353;434,354;535
> > 433,533;443,435;553
> > 453;
> > 534;
> > 543;
> > 444,445;455
> > 454;545
> > 544;554
> > 555;
> >
> > it's just the combinations with repetitions of 3 out of 5 elements in
> > lexicographic order, with the permutations written below the cases.
> >
> >
> > 1 3 3 3 3 3 3|3 6 6 6 6 6 3 6 6 6 6 3 6 6 6 3 6 6 3 6 3 ... 7 [28]
> > (3 out of 7 elements)
> > 7
> > 1 3 3 3 3 3|3 6 6 6 6 3 6 6 6 3 6 6 3 6 3 ... 6 [21]
> > (3 out of 6 elements)
> > 6
> > 1 3 3 3 3|3 6 6 6 3 6 6 3 6 3 Multinomial coefficient 5 [15] (3
> > out of 5 elements)
> > 5
> > 1 3 3 3|3 6 6 3 6 3 follows Pascal Simplex [10] (3 out
> > of 4 elements)
> > 4
> > 1 3 3|3 6 3 follows Pascal's Tetrahedron(last row excl.)[6]
> > (3 out of 3 elements)
> > 3
> > 1 3|3 follows Pascal's Triangle [3] (3 out
> > of 2 elements)
> > 2
> > 1 [1] (3
> > out of 1 element)
> >
> >
> > number of combinations beginning with the 1st element - triangular numbers
> > picking 4 elements with repetition would be governed by tetrahedral numbers
> > and so on
> >
> > HOW COULD ONE GENERATE ALL THIS IN J??
> > thanks in advance
> > atto
> >
> >
> >
> > Lexicographic Multiset Permutation Generation including Ranking etc.
> > A New Method for Generating Permutations in Lexicographic Order
> > http://203.72.2.115/Ejournal/AL03050402.pdf
> > From Permutations to Iterative Permutations
> > http://www.ijcset.net/docs/Volumes/volume2issue7/ijcset2012020702.pdf
> > ----------------------------------------------------------------------
> > 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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