parts {partitions}R Documentation

Enumerate the partitions of an integer

Description

Given an integer, return a matrix whose columns enumerate its partitions.

Function parts() returns the unrestricted partitions; function diffparts() returns the unequal partitions; function restrictedparts() returns the restricted partitions; function blockparts() returns the partitions subject to specified maxima; and function compositions() returns all compositions of the argument.

Usage

parts(n)
diffparts(n)
restrictedparts(n, m, include.zero=TRUE, decreasing=TRUE)
blockparts(f, n=NULL, include.fewer=FALSE)
compositions(n, m=NULL, include.zero=TRUE)

Arguments

n Integer to be partitioned. In function blockparts(), the default of NULL means to return all partitions of any size
m In functions restrictedparts() and compositions(), the order of the partition
include.zero In functions restrictedparts() and compositions(), Boolean with default FALSE meaning to include only partitions of n into exactly m parts; and TRUE meaning to include partitions of n into at most m parts (because zero parts are included)
include.fewer In function blockparts(), Boolean with default FALSE meaning to return vectors whose sum is exactly n and TRUE meaning to return partitions whose sum is at most n
decreasing In restrictedparts(), Boolean with default TRUE meaning to return partitions whose parts are in decreasing order and FALSE meaning to return partitions in lexicographical order, as appearing in Hindenburg's algorithm. Note that setting to decreasing to FALSE has the effect of making conjugate() return garbage
f In function blockparts(), a vector of strictly positive integers that gives the maximal number of blocks; see details

Details

Note

These vectorized functions return a matrix whose columns are the partitions. If this matrix is too large, consider enumerating the partitions individually using the functionality documented in nextpart.Rd.

Author(s)

Robin K. S. Hankin

References

See Also

nextpart

Examples

parts(5)
diffparts(10)
restrictedparts(9,4)
restrictedparts(9,4,FALSE)
restrictedparts(9,4,decreasing=TRUE)

blockparts(1:4)
blockparts(1:4,3)
blockparts(1:4,3,include.fewer=TRUE)

blockparts(c(4,3,3,2),5)  # Knuth's example, Fascicle 3a, p16

compositions(3)


[Package partitions version 1.9-3 Index]