Even Permutations Calculator

Calculate the number of even permutations (the Alternating Group) for a set of size n.

Even Permutations (Alternating Group An)12
Total Permutations (n!)24

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Even vs Odd Permutations

In abstract algebra, any permutation of a set can be broken down into a sequence of "swaps" (transpositions) between two elements. If the number of swaps required is an even number, the permutation is "even".

The Alternating Group

Exactly half of all possible permutations of a set (for n > 1) are even. The set of all even permutations forms a mathematical group known as the Alternating Group, denoted as An.