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Combinatorics (combinatorial analysis) is a branch of mathematics that studies the discrete objects, the set (a combination, permutation, deployment and transfer of elements) and the relationship to them (eg, partial order).

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Trying to implement a simple/efficient combinations function in MATLAB

You can find an implementation in Octave. The function is, as in Matlab, called nchoosek. Documentation is here. For the theory behind this type of algorithms, you can consult section 7.2.1 of Volume …
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