From: Ales Ziberna <aleszib_at_gmail.com>

Date: Fri 09 Dec 2005 - 22:09:06 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Fri Dec 09 22:27:26 2005

Date: Fri 09 Dec 2005 - 22:09:06 EST

As to my knowladge, the function is not located in any packages. If you wish, I can contact the author and ask him, if he is willing to post the function on to the list.

Best,

Ales Ziberna

- Original Message ----- From: "Ingmar Visser" <I.Visser@uva.nl> To: "Ales Ziberna" <aleszib@gmail.com>; "R-help" <r-help@stat.math.ethz.ch> Sent: Friday, December 09, 2005 9:56 AM Subject: Re: [R] Finding all possible partitions of N units into k classe

Can you tell us which package that function is in? Google on the r-project site nor on the www produced a hit. best, ingmar

> From: "Ales Ziberna" <aleszib@gmail.com>

*> Date: Fri, 9 Dec 2005 09:22:47 +0100
**> To: "R-help" <r-help@stat.math.ethz.ch>
**> Subject: Re: [R] Finding all possible partitions of N units into k classe
**>
**> I would like to thank everybody who replied for their useful suggestions
**> and
**> especially the person who (since you replied privately, I do not know if I
**> may expose your name or function) provided the "nkpartitions" function,
**> that
**> does exactly what I wanted.
**>
**>
**>
**> Thank you all again!
**>
**>
**> Best,
**>
**> Ales Ziberna
**>
**> ----- Original Message -----
**> From: "Ted Harding" <Ted.Harding@nessie.mcc.ac.uk>
**> To: "Ales Ziberna" <aleszib@gmail.com>
**> Cc: "R-help" <r-help@stat.math.ethz.ch>
**> Sent: Thursday, December 08, 2005 5:19 PM
**> Subject: RE: [R] Finding all possible partitions of N units into k classe
**>
**>
**> On 08-Dec-05 Ales Ziberna wrote:
**>> Dear useRs!
**>>
**>> I would like to generate a list of all possible (unique)
**>> partitions of N units into k classes. For example, all possible
**>> partitions of 4 units into 2 classes are (I hope I have not
**>> missed anyone):
**>>
**>> 1,1,1,2 (this can be read as {1,2,3},{4})
**>> 1,1,2,1
**>> 1,2,1,1
**>> 2,1,1,1
**>> 1,1,2,2
**>> 1,2,1,2
**>> 1,2,2,1
**>>
**>> The partitions 1,1,2,2 and 2,2,1,1 are the same and are
**>> therefore not two unique partitions.
**>
**> ... which seems to imply that 2,1,1,1 and 1,2,2,2 are the same,
**> so I would write your list above as
**>
**>> 1,1,1,2 (this can be read as {1,2,3},{4})
**>> 1,1,2,1
**>> 1,2,1,1
**>> 1,2,2,2
**>> 1,1,2,2
**>> 1,2,1,2
**>> 1,2,2,1
**>
**> which should be a clue!
**>
**> Fix the class to which unit "1" belongs as Class 1. This
**> leaves the partitioning of units 2:N, of which there are
**> 2^(N-1) except that you want to exclude the case where they
**> all go into Class 1. So 2^(N-1) -1.
**>
**> So let K = 1:(2^(N-1)-1), and for each k in K make the binary
**> representation of k. Say this gives N-1 binary digits
**>
**> i1 i2 ... i[N-1]
**>
**> (note that none of these will have all binary digits = 0).
**>
**> Then assign unit "j+1" to Class 1 if ij = 0, otherwise to
**> Class 2.
**>
**> However, that is if you want to do it with your bare hands!
**> The package combinat contains also the function 'hcube' which
**> can be readily adapted to do just that (since it initially
**> generates all the 2^N combinations of the above).
**>
**> library(combinat)
**> ?hcube
**>
**> x<-rep(2,4) # for partitions of 4 units into classes {1,2}
**>
**> hcube(x,scale=1,transl=0)
**> # [,1] [,2] [,3] [,4]
**> # [1,] 1 1 1 1
**> # [2,] 2 1 1 1
**> # [3,] 1 2 1 1
**> # [4,] 2 2 1 1
**> # [5,] 1 1 2 1
**> # [6,] 2 1 2 1
**> # [7,] 1 2 2 1
**> # [8,] 2 2 2 1
**> # [9,] 1 1 1 2
**> # [10,] 2 1 1 2
**> # [11,] 1 2 1 2
**> # [12,] 2 2 1 2
**> # [13,] 1 1 2 2
**> # [14,] 2 1 2 2
**> # [15,] 1 2 2 2
**> # [16,] 2 2 2 2
**>
**> ### Note, by following the "2"s, that this is counting in binary
**> ### from 0 to 2^N - 1, with "1" for 0 and "2" for 1 and least
**> ### significant bit on the left, so it does what is described
**> ### above. But we need to manipulate this, so assign it to K:
**>
**> K<-hcube(x,scale=1,transl=0)
**>
**> ### Now select only thos which assign unit "1" to Class 1:
**>
**> K[K[,1]==1,]
**> # [,1] [,2] [,3] [,4]
**> # [1,] 1 1 1 1
**> # [2,] 1 2 1 1
**> # [3,] 1 1 2 1
**> # [4,] 1 2 2 1
**> # [5,] 1 1 1 2
**> # [6,] 1 2 1 2
**> # [7,] 1 1 2 2
**> # [8,] 1 2 2 2
**>
**> of which you need to leave off the first, so, finally:
**>
**> N<-4 ### Or general N at this point
**>
**> x<-rep(2,N)
**>
**> K<-hcube(x,scale=1,transl=0)
**>
**> K[K[,1]==1,][-1,]
**> # [,1] [,2] [,3] [,4]
**> # [1,] 1 2 1 1
**> # [2,] 1 1 2 1
**> # [3,] 1 2 2 1
**> # [4,] 1 1 1 2
**> # [5,] 1 2 1 2
**> # [6,] 1 1 2 2
**> # [7,] 1 2 2 2
**>
**>
**> That looks like it!
**>
**> Best wishes,
**> Ted.
**>
**>
**> --------------------------------------------------------------------
**> E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk>
**> Fax-to-email: +44 (0)870 094 0861
**> Date: 08-Dec-05 Time: 16:19:24
**> ------------------------------ XFMail ------------------------------
**>
**> ______________________________________________
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**> PLEASE do read the posting guide!
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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Fri Dec 09 22:27:26 2005

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