Extremum-count conjecture for average normalized Penrose–Banzhaf power indices
Extremum-count conjecture. For every k=1,…,nk=1,\ldots,nk=1,…,n, the function q↦E(\Greekmath010Ck↓)q\mapsto\mathbb{E}({\Greekmath 010C}_k^{\downarrow})q↦E(\Greekmath010Ck↓) has exactly k−1k-1k−1 local extrema on (1/2,1)(1/2,1)(1/2,1).