nchoose

all combinations of the elements of a set

W = nchoose(S) returns all possible combinations of 0, 1, or more
elements of the set S, having N elements. There are 2^N combinations
in total. W is a cell array and each cell holds one of these
combination (as a row vector).
S can be a cell array, and each cell of W will then contain a cell
array. W is the powerset of S, as it includes the empty set (0
elements) as it first cell.

For a vector of integers I, W = nchoose(S, I) returns only the sets
indicated by the indices I. This might be useful for large sets.

Examples:
nchoose([2 4 6 8])
% -> { [] ;
% [2] ;
% [4] ;
% [2 4] ;
% [6] ;
% ...
% [2 6 8] ;
% [4 6 8] ;
% [2 4 6 8]} ; % in total 16 different combinations

nchoose([33 22 11], [1 8 4])
% -> { [] ; [33 22 11] ; [ 33 11]}

Notes:
- For sets containing more than 18 elements a warning is given, as this
can take some time. Hit Ctrl-C to intterupt calculations.
- If S contain non-unique elements (e.g. S = [1 1 2]), nchoose will
return non-unique cells. In other words, nchoose treats all elements
of S as being unique. One could use nchoose(UNIQUE(S)) to avoid that.
- Loosely speaking, nchoose(S) collects all output of multiple calls to
NCHOOSEK(S, K) where K is looping from 1 to the number of elements of
S. The implementation of nchoose, however, does rely of a different
method and is much faster than such a loop.
- For more information, see: http://en.wikipedia.org/wiki/Power_set

See also nchoosek, perms,
permn, nchoose2, allcomb on the file Exchange