Compositions generator

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

compositions(n, k = NULL, 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
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 compositions required, usually used with skip
skip	the number of compositions skipped
index	a vector of indices of the desired compositions
nsample	sampling random compositions
drop	vectorize a matrix or unlist a list

See also

icompositions for iterating compositions and ncompositions to calculate number of compositions

Examples

# all compositions of 4
compositions(4)
#>      [,1] [,2] [,3] [,4]
#> [1,]    1    1    1    1
#> [2,]    1    1    2    0
#> [3,]    1    2    1    0
#> [4,]    1    3    0    0
#> [5,]    2    1    1    0
#> [6,]    2    2    0    0
#> [7,]    3    1    0    0
#> [8,]    4    0    0    0
# reversed lexicographical order
compositions(4, descending = TRUE)
#>      [,1] [,2] [,3] [,4]
#> [1,]    4    0    0    0
#> [2,]    3    1    0    0
#> [3,]    2    2    0    0
#> [4,]    2    1    1    0
#> [5,]    1    3    0    0
#> [6,]    1    2    1    0
#> [7,]    1    1    2    0
#> [8,]    1    1    1    1

# fixed number of parts
compositions(6, 3)
#>       [,1] [,2] [,3]
#>  [1,]    1    1    4
#>  [2,]    1    2    3
#>  [3,]    1    3    2
#>  [4,]    1    4    1
#>  [5,]    2    1    3
#>  [6,]    2    2    2
#>  [7,]    2    3    1
#>  [8,]    3    1    2
#>  [9,]    3    2    1
#> [10,]    4    1    1
# reversed lexicographical order
compositions(6, 3, descending = TRUE)
#>       [,1] [,2] [,3]
#>  [1,]    4    1    1
#>  [2,]    3    2    1
#>  [3,]    3    1    2
#>  [4,]    2    3    1
#>  [5,]    2    2    2
#>  [6,]    2    1    3
#>  [7,]    1    4    1
#>  [8,]    1    3    2
#>  [9,]    1    2    3
#> [10,]    1    1    4

# column major
compositions(4, layout = "column")
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,]    1    1    1    1    2    2    3    4
#> [2,]    1    1    2    3    1    2    1    0
#> [3,]    1    2    1    0    1    0    0    0
#> [4,]    1    0    0    0    0    0    0    0
compositions(6, 3, layout = "column")
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#> [1,]    1    1    1    1    2    2    2    3    3     4
#> [2,]    1    2    3    4    1    2    3    1    2     1
#> [3,]    4    3    2    1    3    2    1    2    1     1

# list output
compositions(4, layout = "list")
#> [[1]]
#> [1] 1 1 1 1
#> 
#> [[2]]
#> [1] 1 1 2
#> 
#> [[3]]
#> [1] 1 2 1
#> 
#> [[4]]
#> [1] 1 3
#> 
#> [[5]]
#> [1] 2 1 1
#> 
#> [[6]]
#> [1] 2 2
#> 
#> [[7]]
#> [1] 3 1
#> 
#> [[8]]
#> [1] 4
#> 
compositions(6, 3, layout = "list")
#> [[1]]
#> [1] 1 1 4
#> 
#> [[2]]
#> [1] 1 2 3
#> 
#> [[3]]
#> [1] 1 3 2
#> 
#> [[4]]
#> [1] 1 4 1
#> 
#> [[5]]
#> [1] 2 1 3
#> 
#> [[6]]
#> [1] 2 2 2
#> 
#> [[7]]
#> [1] 2 3 1
#> 
#> [[8]]
#> [1] 3 1 2
#> 
#> [[9]]
#> [1] 3 2 1
#> 
#> [[10]]
#> [1] 4 1 1
#> 

# zero sized compositions
dim(compositions(0))
#> [1] 1 0
dim(compositions(5, 0))
#> [1] 0 0
dim(compositions(5, 6))
#> [1] 0 6
dim(compositions(0, 0))
#> [1] 1 0
dim(compositions(0, 1))
#> [1] 0 1