5 problems

In the infinite group problem, let $\pi$ be a continuous piecewise linear extreme function, and let its slopes be the slopes of its linear pieces. 4-slope conjecture. The function…

Let $\pi\colon \mathbb R^k\to\mathbb R$ be an extreme function or a facet. Piecewise-linear approximation conjecture. Every extreme function, respectively facet, $\pi$ is either pi…

Let $\pi\colon \mathbb R\to\mathbb R$ be a minimal function, meaning a minimal valid function for the single-row problem, and suppose that $\pi$ is absolutely continuous and that i…

Let $\pi\colon \mathbb R\to\mathbb R$ be an absolutely continuous extreme function. A simple function takes only finitely many values almost everywhere. Generalized simple-derivati…

Let $\pi$ be a minimal valid function for $R_f(\mathbb R^2,\mathbb Z^2)$ that is piecewise linear and continuous on $\mathcal P_q$. The function $\pi$ is diagonally constrained if,…