The aim of this paper is to improve the large deviation principle for the number of descents in a random permutation by establishing a sharp large deviation principle of any order. We shall also prove a sharp large deviation principle of any order for the major index in a random permutation.

翻译：本文旨在通过建立任意阶的尖锐大偏差原理，改进随机排列中逆序数的大偏差原理。我们还将证明随机排列中主指标数的任意阶尖锐大偏差原理。