[Jprogramming] Bell numbers

[R.E. Boss]

Thanks very much, I appreciate your kindness.


R.E. Boss


> -----Oorspronkelijk bericht-----
> Van: programming-bounces at jsoftware.com [mailto:programming-
> bounces at jsoftware.com] Namens bill lam
> Verzonden: dinsdag 18 december 2007 4:13
> Aan: Programming forum
> Onderwerp: Re: [Jprogramming] Bell numbers
> 
> This article is not available online.
>   http://www.vector.org.uk/archive/v171/
> 
> The following is part of listing from my vector hard copy.
> NB. ==============================
> s2nr from Iverson's Concrete Math Companion to generate subset numbers.
>     s2nr=: |:@(^/~ %. ^!._1/~)@i."0
>     ]a=. s2nr 10x
> 1 0   0    0    0    0    0   0  0 0
> 0 1   0    0    0    0    0   0  0 0
> 0 1   1    0    0    0    0   0  0 0
> 0 1   3    1    0    0    0   0  0 0
> 0 1   7    6    1    0    0   0  0 0
> 0 1  15   25   10    1    0   0  0 0
> 0 1  31   90   65   15    1   0  0 0
> 0 1  63  301  350  140   21   1  0 0
> 0 1 127  966 1701 1050  266  28  1 0
> 0 1 255 3025 7770 6951 2646 462 36 1
>     ]b=. |: 1 1 }.a
> 1 1 1 1  1  1   1    1    1
> 0 1 3 7 15 31  63  127  255
> 0 0 1 6 25 90 301  966 3025
> 0 0 0 1 10 65 350 1701 7770
> 0 0 0 0  1 15 140 1050 6951
> 0 0 0 0  0  1  21  266 2646
> 0 0 0 0  0  0   1   28  462
> 0 0 0 0  0  0   0    1   36
> 0 0 0 0  0  0   0    0    1
>     ]c=. b * ! i. #b
> 1 1 1  1  1   1    1     1      1
> 0 1 3  7 15  31   63   127    255
> 0 0 2 12 50 180  602  1932   6050
> 0 0 0  6 60 390 2100 10206  46620
> 0 0 0  0 24 360 3360 25200 166824
> 0 0 0  0  0 120 2520 31920 317520
> 0 0 0  0  0   0  720 20160 332640
> 0 0 0  0  0   0    0  5040 181440
> 0 0 0  0  0   0    0     0  40320
>     ]d=. +/ \. c
> 1 2 6 26 150 1082 9366 94586 1091670
> 0 1 5 25 149 1081 9365 94585 1091669
> 0 0 2 18 134 1050 9302 94458 1091414
> 0 0 0  6  84  870 8700 92526 1085364
> 0 0 0  0  24  480 6600 82320 1038744
> 0 0 0  0   0  120 3240 57120  871920
> 0 0 0  0   0    0  720 25200  554400
> 0 0 0  0   0    0    0  5040  221760
> 0 0 0  0   0    0    0     0   40320
> 
> NB. ==============================
> 
> In particular, row (column?) sum of a is bell numbers
>     +/"1 a
> 1 1 2 5 15 52 203 877 4140 21147
> 
> R.E. Boss wrote:
> > Where are these articles available?
> > The first is not in http://www.jsoftware.com/jwiki/Articles
> >
> >
> > R.E. Boss
> >
> >
> >> -----Oorspronkelijk bericht-----
> >> Van: programming-bounces at jsoftware.com [mailto:programming-
> >> bounces at jsoftware.com] Namens bill lam
> >> Verzonden: maandag 17 december 2007 15:41
> >> Aan: Programming forum
> >> Onderwerp: Re: [Jprogramming] Bell numbers
> >>
> >> FYI, Eugene McDonnell contributed an article in Vector
> >>   McDonnell, Eugene, At Play with J: Blists in OLEIS, Vol 17.1, 110
> >> and a technical correspondence in Vol 17.2, 112
> >> It shows Bell number is the row sum of Stirling subset numbers.
> >>
> >> Joseph De Kerf discussed calculation of Bell number using floating
> point
> >> in APL,
> >>   De Kerf, Joseph, Bell Numbers and APL, Vol 17.1, 131
> >>
> >> --
> >> regards,
> >> bill
> >> ----------------------------------------------------------------------
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> >
> > ----------------------------------------------------------------------
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> >
> 
> 
> --
> regards,
> bill
> ----------------------------------------------------------------------
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