Problem

Source: Mongolian TST2008 day4 problem2

Tags: combinatorics proposed, combinatorics



Let $ a_1,a_2,...,a_n$ is permutaion of $ 1,2,...,n$. For this permutaion call the pair $ (a_i,a_j)$ wrong pair if $ i<j$ and $ a_i >a_j$.Let number of inversion is number of wrong pair of permutation $ a_1,a_2,a_3,..,a_n$. Let $ n \ge 2$ is positive integer. Find the number of permutation of $ 1,2,..,n$ such that its number of inversion is divisible by $ n$.