Bounds on Normal Approximation for Descents and Inversions of Random Permutations

Abstract

In this work, there are two objectives. First, we find the explicit constants for uniform bounds on normal approximation of the number of descents and the number of inversions given by Fulman (2004). Second, we give new bounds of such approximations. We give both uniform and non-uniform bounds. For uniform bounds we give constants which are better than Fulman’s constants. In the part of non-uniform bounds we present both linear and exponential bounds.