partitions {arrangements}

Partitions generator

Description

This function partitions an non-negative interger n into k parts or parts of any sizes. The results are in lexicographical or reversed lexicographical order.

Usage

partitions(n, k = NULL, distinct = FALSE, descending = FALSE,
  layout = NULL, nitem = -1L, skip = NULL, index = NULL,
  nsample = NULL, drop = NULL)

Arguments

n

an non-negative integer to be partitioned

k

number of parts

distinct

an logical to restrict distinct values

descending

an logical to use reversed lexicographical order

layout

if "row", "column" or "list" is specified, the returned value would be a "row-major" matrix, a "column-major" matrix or a list respectively

nitem

number of partitions required, usually used with skip

skip

the number of partitions skipped

index

a vector of indices of the desired partitions

nsample

sampling random partitions

drop

vectorize a matrix or unlist a list

See Also

ipartitions for iterating partitions and npartitions to calculate number of partitions

Examples

# all partitions of 6
partitions(6)
# reversed lexicographical order
partitions(6, descending = TRUE)

# fixed number of parts
partitions(10, 5)
# reversed lexicographical order
partitions(10, 5, descending = TRUE)

# column major
partitions(6, layout = "column")
partitions(6, 3, layout = "column")

# list output
partitions(6, layout = "list")
partitions(6, 3, layout = "list")

# zero sized partitions
dim(partitions(0))
dim(partitions(5, 0))
dim(partitions(5, 6))
dim(partitions(0, 0))
dim(partitions(0, 1))