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So basically what am looking for is an operation that you can apply to various terms, whereby all the permutations of said terms are then derived.

So if such an operation was denoted by ●, it would be as follows:

1●2●3 = {123, 132, 213, 231, 312, 321}.

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    Your title and your question are asking two different things.2017-02-03
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    Perhaps you are looking for $S_n$, the group of permutations of the set $\{1,2,...,n\}$. Or perhaps $\text{Sym}(M)$, the group of permutations of a general set $M$. https://en.wikipedia.org/wiki/Permutation_group2017-02-03

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