Alon–Hefetz–Krivelevich–Tyomkyn 1/e inducibility conjecture for graphs

For an $n$-vertex graph $G$, let $X_{G,k}$ be the number of edges induced by a uniformly random $k$-vertex subset of $G$. Define

$$I(n,k,\ell)=\max\{\Pr(X_{G,k}=\ell):|V(G)|=n\}$$

and

$$\operatorname{ind}(k,\ell)=\lim_{n\to\infty}I(n,k,\ell).$$

Alon–Hefetz–Krivelevich–Tyomkyn's 1/e conjecture. For all $0<\ell<\binom{k}{2}$ we have

$$\operatorname{ind}(k,\ell)\le 1/e+o_k(1).$$

This conjecture concerns the maximum asymptotic point probability for the edge count in a random induced subgraph, and predicts a universal upper bound of $1/e$ away from the empty and complete cases. Its status is not resolved in the supplied text.