Bounds on Normal Approximations for the number of Descents and Inversions

Abstract

In this article, we use Stein’s method to give non uniform bounds for normal approximation for the number of descents and inversions. Moreover, we also improve a constant on uniform bounds for normal approximation of those random variables in Fulman’s work in 2004. Our constants are 13.42 and 14.24, respectively.

Keywords:

• Descent
• Inversion
• Permutation
• Stein’s method

Mathematics Subject Classification::

• 60F05