# [R] Partition of a set

Michael Bedward michael.bedward at gmail.com
Fri Nov 12 11:42:22 CET 2010

```Hi Diane,

Does this do what you want ?

listParts <- function(n) {
# Generates a list of lists representing the partitions
# of an integer n
require(partitions)
x <- 1:n
apply(setparts(n), 2, function(pp) tapply(x, pp, function(xx) list(xx)))
}

Michael

On 12 November 2010 21:15, Diana Tichy
<d.tichy at mathematik.uni-wuerzburg.de> wrote:
> Hello Michael
> once again. Now I can use print.partition which tells me, how to generate,
> e.g., all possible 5 partitions of {1,2,3}. But this generation is still
> complicated. Does there already exist a function doing that for me, e.g.
> returns a list, where the first element contains the one-elemnt partion, the
> second to fourth the three 2-element-partions and the fifth the 3-element
> partition?
> Do you know or is it my job to implement this by myself (o.k. but
> time-consuming ..)
>
> Best wishes
> Diana
>
> Am 12.11.2010 10:32, schrieb Michael Bedward:
>>
>> Hi Diana,
>>
>> Have a look at the setparts function in the partitions package.
>>
>> Michael
>>
>> On 12 November 2010 20:03, Diana<d.tichy at mathematik.uni-wuerzburg.de>
>>  wrote:
>>>
>>> Hi
>>>
>>> I am new on this forum. I am searching for a function in R which provides
>>> all partitions of a set, say for the set
>>> {1,2,3}
>>> you get
>>> {{1,2,3}}
>>> {1,{2,3}}
>>> {2,{1,3}}
>>> {3,{1,2}}
>>> {{1},{2},{3}}
>>> . The number of partitions of a set is given by Bellsche`s number. The
>>> number of possibilities of length (this is the number of subsets included
>>> in
>>> the partition) of the partition is given by the partition function.
>>> But I need a list containg all possible partitions of an index set
>>> {1,...,d}, d arbitrary.
>>>
>>>
>>> Can anybody help me?
>>>
>>> Thanks a lot!
>>> Diana Tichy
>>> --
>>> View this message in context:
>>> http://r.789695.n4.nabble.com/Partition-of-a-set-tp3039291p3039291.html
>>> Sent from the R help mailing list archive at Nabble.com.
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>
> --
> Diana Tichy (geb. Stöhr)
> Lehrstuhl für Statistik
> Institut für Mathematik
> Universität Würzburg
> Am Hubland
> 97074 Würzburg
> Raum R110, Mathematikgebäude
> Tel.: 0931-31 85027
> d.tichy at mathematik.uni-wuerzburg.de
> http://statistik.mathematik.uni-wuerzburg.de/~tichy
>
>

```