The sensitivity conjecture, induced subgraphs of cubes, and Clifford algebras

Abstract

We give another version of Huang’s proof that an induced subgraph of the $n$-dimensional cube graph containing over half the vertices has maximal degree at least $\sqrt{n}$, which implies the Sensitivity Conjecture. This argument uses Clifford algebras of positive definite signature in a natural way. We also prove a weighted version of the result.