Sharp Inner Product Correlations for Hypercube Bijections

Ijay Narang, Muchen Ju

We resolve a conjecture of Rob Morris concerning bijections on the hypercube. Specifically, we show that for any bijection $f:\{-1,1{\}}^n\to \{-1,1{\}}^n$, \[ \Pr_{x,y \in \{-1,1\}…