Independent sets of a given size and structure in the hypercube

Matthew Jenssen, Will Perkins, Aditya Potukuchi

We determine the asymptotics of the number of independent sets of size $\lfloor \beta 2^{d-1}\rfloor$ in the discrete hypercube $Q_d=\{0,1{\}}^d$ for any fixed $\beta \in [0,1]$ as $d \to \…