Algebra From Geometry in the Card Game SET. (1st September 2016) - Goldberg, Timothy E.
Summary: The card game SET has often been studied as a rich source of combinatorial and probabilistic questions and also as a beautiful and hands-on example of a finite geometry. In fact, SET also possesses an interesting algebraic structure: There is a natural binary operation on the cards in SET that is commutative but possesses no identity and is not even associative. This structure was previously introduced and studied in a paper by Holdener in 2005 by assigning coordinates to the SET cards using the integers modulo 3. Here, we obtain similar results with an entirely different approach, coordinate free and based solely on the geometric structure of SET. The algebraic structure is defined and many of its properties demonstrated, including a proof that SET has the structure of an involutary quandle.