A central limit theorem for a new statistic on permutations

TL;DR

This paper establishes a central limit theorem for a new permutation statistic, introduces a novel proof approach, and highlights the contributions of B. V. Rao in the context of permutation analysis.

Contribution

It introduces a new permutation statistic and a general approach for proving central limit theorems, expanding the theoretical understanding of permutation distributions.

Findings

Proves a CLT for the new permutation statistic

Demonstrates a new method for CLT proofs

Highlights the significance of B. V. Rao's work

Abstract

This paper does three things: It proves a central limit theorem for novel permutation statistics (for example, the number of descents plus the number of descents in the inverse). It provides a clear illustration of a new approach to proving central limit theorems more generally. It gives us an opportunity to acknowledge the work of our teacher and friend B. V. Rao.