The number of 4-colorings of the Hamming cube

Jeff Kahn, Jinyoung Park

Let $Q_d$ be the $d$-dimensional hypercube and $N=2^d$. We prove that the number of (proper) 4-colorings of $Q_d$ is asymptotically \[6e2^N,\] as was conjectured by Engbers and Gal…