indexpermutation

An index permutation is a fundamental concept in combinatorics and computer science, referring to a specific arrangement or ordering of a sequence of indices. Essentially, it's a way to reorder the elements of a list or array by specifying a new sequence of positions. If you have a list of length n, an index permutation is a sequence of length n containing each integer from 0 to n-1 exactly once. This permutation can then be used to access or rearrange the elements of the original list in the new order.

For example, if we have a list `[a, b, c]` (with indices 0, 1, 2), an index permutation `[2, 0, 1]` would result in the reordered list `[c, a, b]`. The first element of the new list is the element at index 2 of the original list, the second element is from index 0, and the third from index 1. Index permutations are crucial in algorithms that involve shuffling, sorting, and data manipulation, as they provide a direct mechanism for controlling the order of operations on data structures. They are also closely related to the mathematical concept of permutations of a set. The total number of distinct index permutations for a set of n elements is n factorial (n!).