The clique-coclique inequality states that for a graph $G$ on $n$ vertices that is either distance-regular or vertex-transitive, the independence number $\alpha(G)$ and the clique number $\omega(G)$ satisfy $$ \alpha(G) \omega(G)\le n. $$ The uncertainty inequality (well, one of its numerous variations) states that for an abelian group $G$ of order $n$, and any function $f\in L(G)$, the support of $f$ and that of its Fourier transform $\hat f$ satisfy $$ |\mathrm{supp} f||\mathrm{supp}\hat f|\ge n. $$
Even though the inequalities go in opposite directions, they manifest a striking similarity. Is this a mere coincidence, or there is a hidden reason for them to be similar?
