New permutation statistics: Variation and a variant

For each permutation pi we introduce the variation statistic of pi, as the total number of elements on the right between each two adjacent elements of pi. 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 according to the variation statistic, and for that according to the modified version. (C) 2009 Elsevier B.V. All rights reserved.Mathematics, AppliedSCI(E)EI0ARTICLE81974-197815