



















In this note we give a version of Hao Huang's proof of the sensitivity conjecture, shedding some light on the origin of the magical matrix $A$ in that proof. For the history of the subject and the importance of this conjecture to the study of boolean functions, we refer to the original paper. Here we only state the main result: Consider the boolean cube $Q_n=\{0,1\}^n$ as a graph, whose edges connect pairs of vertices differing in one coordinate. Then any its induced subgraph on greater than $2^{n-1}$ (the half) vertices has degree of some vertex at least $\sqrt{n}$.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。