For example, if I have a set of all permutations of the set {1, 2, 3, 4} and the permutation 1, 4, 3, 2 how do i calculate which element of the set it is without calculating all the permutations?
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Well, how are you listing the permutations? If lexicographic, then count those that begin with $1$, and so on. – lulu Feb 12 '24 at 13:54
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See also the reverse, https://math.stackexchange.com/questions/2717475/finding-position-of-specific-permutation-in-alphabetically-ordered-list-of-permu?noredirect=1&lq=1 – JMoravitz Feb 12 '24 at 13:56