In-person Math Counts October 2025 - Groups and their graphs

Continuing our exploration of abstract Group Theory. I hope to finally explore the action of the symmetric group on 3 elements on an equilateral triangle, and its graphic representation as a Cayley Graph.

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I will also do a quick recap of my "improv" or "desert island" approach to exploring mathematics. This is a work in progress, and an experiment. I am hinting at a thesis that mathematics is a self-correcting code, where partially remembered or even mis-remembered axioms, definitions and theorems will converge to something equivalent to the "standard" accepted axioms, definitions, and theorems.