Determine all n-tuples using the elements of a set.

Determine all n-tuples using the elements of a set. This is really just a simple wrapper for expand.grid, so it is not optimized.

tuples(set, n = length(set), repeats = FALSE, list = FALSE)

Arguments

set	a set
n	length of each tuple
repeats	if set contains duplicates, should the result?
list	tuples as list?

Value

a matrix whose rows are the n-tuples

Examples

tuples(1:2, 3)
#>      [,1] [,2] [,3]
#> [1,]    1    1    1
#> [2,]    1    1    2
#> [3,]    1    2    1
#> [4,]    1    2    2
#> [5,]    2    1    1
#> [6,]    2    1    2
#> [7,]    2    2    1
#> [8,]    2    2    2
tuples(1:2, 3, list = TRUE)
#> [[1]]
#> [1] 1 1 1
#> 
#> [[2]]
#> [1] 1 1 2
#> 
#> [[3]]
#> [1] 1 2 1
#> 
#> [[4]]
#> [1] 1 2 2
#> 
#> [[5]]
#> [1] 2 1 1
#> 
#> [[6]]
#> [1] 2 1 2
#> 
#> [[7]]
#> [1] 2 2 1
#> 
#> [[8]]
#> [1] 2 2 2
#> 

apply(tuples(c("x","y","z"), 3), 1, paste, collapse = "")
#>  [1] "xxx" "xxy" "xxz" "xyx" "xyy" "xyz" "xzx" "xzy" "xzz" "yxx" "yxy" "yxz"
#> [13] "yyx" "yyy" "yyz" "yzx" "yzy" "yzz" "zxx" "zxy" "zxz" "zyx" "zyy" "zyz"
#> [25] "zzx" "zzy" "zzz"

# multinomial coefficients
r <- 2 # number of variables, e.g. x, y
n <- 2 # power, e.g. (x+y)^2
apply(burst(n,r), 1, function(v) factorial(n)/ prod(factorial(v))) # x, y, xy
#> [1] 1 1 2
mp("x + y")^n
#> x^2  +  2 x y  +  y^2

r <- 2 # number of variables, e.g. x, y
n <- 3 # power, e.g. (x+y)^3
apply(burst(n,r), 1, function(v) factorial(n)/ prod(factorial(v)))
#> [1] 1 1 3 3
mp("x + y")^n
#> x^3  +  3 x^2 y  +  3 x y^2  +  y^3

r <- 3 # number of variables, e.g. x, y, z
n <- 2 # power, e.g. (x+y+z)^2
apply(burst(n,r), 1, function(v) factorial(n)/ prod(factorial(v))) # x, y, z, xy, xz, yz
#> [1] 1 1 1 2 2 2
mp("x + y + z")^n
#> x^2  +  2 x y  +  2 x z  +  y^2  +  2 y z  +  z^2