Generate all combinations of the elements of `x`

taken `m`

at a time. If `x`

is a positive integer, returns all
combinations of the elements of `seq(x)`

taken `m`

at a
time. If argument `FUN`

is not `NULL`

, applies a function given
by the argument to each point. If simplify is FALSE, returns
a list; otherwise returns an `array`

, typically a
`matrix`

. `...`

are passed unchanged to the
`FUN`

function, if specified.

`combn(x, m, FUN = NULL, simplify = TRUE, …)`

x

vector source for combinations, or integer `n`

for
`x <- seq_len(n)`

.

m

number of elements to choose.

FUN

function to be applied to each combination; default
`NULL`

means the identity, i.e., to return the combination
(vector of length `m`

).

simplify

logical indicating if the result should be simplified
to an `array`

(typically a `matrix`

); if
FALSE, the function returns a `list`

. Note that when
`simplify = TRUE`

as by default, the dimension of the result is
simply determined from `FUN(`

(for
efficiency reasons). This will badly fail if `1st combination`)`FUN(u)`

is not of
constant length.

…

optionally, further arguments to `FUN`

.

A `list`

or `array`

, see the `simplify`

argument above. In the latter case, the identity
`dim(combn(n, m)) == c(m, choose(n, m))`

holds.

Factors `x`

are accepted.

Nijenhuis, A. and Wilf, H.S. (1978)
*Combinatorial Algorithms for Computers and Calculators*;
Academic Press, NY.

`choose`

for fast computation of the *number* of
combinations. `expand.grid`

for creating a data frame from
all combinations of factors or vectors.

# NOT RUN { combn(letters[1:4], 2) (m <- combn(10, 5, min)) # minimum value in each combination mm <- combn(15, 6, function(x) matrix(x, 2, 3)) stopifnot(round(choose(10, 5)) == length(m), c(2,3, round(choose(15, 6))) == dim(mm)) ## Different way of encoding points: combn(c(1,1,1,1,2,2,2,3,3,4), 3, tabulate, nbins = 4) ## Compute support points and (scaled) probabilities for a ## Multivariate-Hypergeometric(n = 3, N = c(4,3,2,1)) p.f.: # table.mat(t(combn(c(1,1,1,1,2,2,2,3,3,4), 3, tabulate, nbins = 4))) ## Assuring the identity for(n in 1:7) for(m in 0:n) stopifnot(is.array(cc <- combn(n, m)), dim(cc) == c(m, choose(n, m))) # }