An Experimental (yet fully rigorous!) Study of a certain "Measure Of Disarray" that 12-year Noga Alon Proved was always Even

TL;DR

This paper investigates a permutation statistic originally proved to always be even by Noga Alon, using a rigorous empirical approach that challenges the notion that mathematics is solely deductive.

Contribution

It introduces a fully rigorous empirical methodology to study permutation statistics, providing new insights into Alon's theorem and addressing misconceptions about mathematical proof.

Findings

Empirical evidence supporting Alon's theorem

Methodology demonstrating rigorous empirical analysis in mathematics

Revisions incorporating feedback from experts

Abstract

We study in depth a certain permutation statistic that was the subject of a brilliant insight by 12-year-old Noga Alon. Our approach is purely empirical and experimental, yet it is fully rigorous, thereby debunking, yet another time, the myth that mathematics is always a deductive science. This revised version contains three postscripts describing improvements pointed out by Stoyan Dimitrov, Kyle Petersen, and Martin Rubey.