2 problems

Let $\mathbf{v}=(v_1,v_2,v_3)$ satisfy $v_1<v_2<v_3$ with each $v_i\in[0,\sqrt{2}]$. Let $\mathbf{\Omega}_{\mathbf{v}}^{(4)}$ be the associated four-cell partition, let…

Convexity and endpoint maximum conjecture. The sequence $(a_i)_{1\leq i\leq n-1}$ is convex. It is strictly increasing when $\ell=2$, and only when $\ell=2$. Moreover, there exists…