2017 USAMO Problems/Problem 2
Problem
Let be a collection of positive integers, not necessarily distinct. For any sequence of integers and any permutation of , define an -inversion of to be a pair of entries with for which one of the following conditions holds:
or Show that, for any two sequences of integers and , and for any positive integer , the number of permutations of having exactly -inversions is equal to the number of permutations of having exactly -inversions.