The exceptional automorphism of $S_6$ explained with colored maps

Abstract: Among all symmetric groups, $S_6$ is the only one with a nontrivial outer automorphism, In this talk, I will describe a new way to understand the exotic embedding of $S_5 \hookrightarrow S_6$ in terms of $5$-colored complete regular maps on the torus. This provides a visual explanation for the existence of the exceptional automorphism of $S_6$.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)