New permutation statistics: Variation and a variant
For each permutation ? ? we introduce the variation  statistic of ? ? , as the total number of elements on the right between each two adjacent elements of ? ? . We modify this new statistic to get a slightly different variant, which behaves more closely like Mahonian statistics such as maj . In this paper we find an explicit formula for the generating function for the number of permutations of length n n according to the variation statistic, and for that according to the modified version.
permutation statistics mahonian generating functions variation statistic kernel method