What is the official name of a specific type of combination algorithm Say that I have the following set of variables:

[A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z]

The values represent a list of variables from a dataset.  Each variable has a certain level of correlation with the target variable $.  The correlation increases or decreases depending on the sort of combination you use against your target $.  For example, BCJX might have a higher correlation with $ than OQTVW.  I'm going to test each possible combination against the training algorithm and output it all, with their accuracy score, in a concise CSV file.  But I don't know the name of the algorithm that might combine these variables in every possible way.

In other words, I want to find the combination with the highest correlation value and the smallest dimension.
You are probably looking for subsets of a set. If a set has $n$ elements, it has $2^n$ subsets when counting also the empty set (there is a clear correspondence to all bit strings of length $n$). So if in your case $n=26$, there are about 67 million subsets of variables to check which might be unfeasible.