The graphic nature of the symmetric group

TL;DR

This paper explores a unique class of exponential sums linked to symmetric groups, revealing their striking visual features and introducing them as a new class of supercharacters with potential mathematical significance.

Contribution

It introduces a novel class of supercharacters derived from exponential sums associated with symmetric groups, highlighting their visual appeal and mathematical novelty.

Findings

Exponential sums exhibit diverse and visually appealing features.

These sums form a new class of supercharacters.

The work uncovers the mathematical structure behind these visual patterns.

Abstract

We investigate a remarkable class of exponential sums which are derived from the symmetric groups and which display a diverse array of visually appealing features. Our interest in these expressions stems not only from their astounding visual properties, but also from the fact that they represent a novel and intriguing class of supercharacters.