nchoosekcom

NCHOOSEK with its complementary combinations

NCHOOSEKCOM Binomial coefficient or all combinations, and its complement

With one output argument, C = NCHOOSEKCOM (..) is the same as C = NCHOOSEK(..). For a vector V, C = NCHOOSEKCOM(V, K) returns a matrix with all possible combinations of the elements of V, taken K at a time. See NCHOOSEK for details.

With two output arguments, [C, D] = NCHOOSEKCOM (V, K) also returns the complementary combinations in D. C and D have the same number of rows: when the j-th row of C contains a combination of K elements of V, then the j-th row of D contains the other elements. In other words, [C(j,:) D(j,:)] is the same as V, except for order.

For a positive scalar N, [C D] = nchoosekcom(N, K) will return the binomial coefficient (= N!/K!(N-K)!) in both C and D, since the number of combinations of N things taken K at a time equals the number of combinations of N things taken (N-K) at a time.

Example:
[C, D] = nchoosekcom(1:5, 2)
% C: - D:
% 1 2 - 3 4 5
% 1 3 - 2 4 5
% 1 4 - 2 3 5
% ..
% 3 4 - 1 2 5
% 3 5 - 1 2 4
% 4 5 - 1 2 3