Combinatorial Aspects of Clifford Algebra

In this paper we focus on some combinatorial aspects of Clifford algebra and show how this algebra allows combinatorial theorems - like e.g. Sperner's lemma - to be "built into the algebraic background", and become part of the structure of the algebra itself. We also give an example of how cumbersome combinatorial proofs can be "mechanized" and carried out in a purely computational manner.