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
> ----------------------------------------------------------------------
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