combn {utils}  R Documentation 
Generate All Combinations of n Elements, Taken m at a Time
Description
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.
Usage
combn(x, m, FUN = NULL, simplify = TRUE, ...)
Arguments
x 
vector source for combinations, or integer 
m 
number of elements to choose. 
FUN 
function to be applied to each combination; default

simplify 
logical indicating if the result should be simplified
to an 
... 
optionally, further arguments to 
Details
Factors x
are accepted.
Value
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.
Author(s)
Scott Chasalow wrote the original in 1994 for S;
R package combinat and documentation by Vince Carey
stvjc@channing.harvard.edu;
small changes by the R core team, notably to return an array in all
cases of simplify = TRUE
, e.g., for combn(5,5)
.
References
Nijenhuis, A. and Wilf, H.S. (1978) Combinatorial Algorithms for Computers and Calculators; Academic Press, NY.
See Also
choose
for fast computation of the number of
combinations. expand.grid
for creating a data frame from
all combinations of factors or vectors.
Examples
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), is.array(m), # 1dimensional
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
## MultivariateHypergeometric(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)),
identical(cc, combn(n, m, identity))  m == 1)