Stirling numbers of the first kind are used to count the number of cycles in these operations.
Zolotarev defined the Jacobi symbol in terms of the parity of this operation. The Schensted correspondence relates a pair of Young tableaux and an output of this operation. Frobenius names a group whose members are the output of this operation on a finite group. Stirling numbers of the first kind are used to count the number of cycles in these operations. The group of all of these operations on a set is the (*) symmetric group. Subtypes of this general operation include inversions, derangements, and transpositions. This operation is given by the bijective mapping of members of a set to itself. The number of these operations for n distinct objects is n factorial. For 10 points, name this operation, the rearrangement of a set of items such that order matters, unlike a combination.
Zolotarev defined the Jacobi symbol in terms of the parity of this operation.
permutation [prompt on factorial] &lt;JL, Math&gt;