5 problems

Let $X$ be a ladder consisting of two rays joined at height $0$ and rungs of lengths $l_m\in\mathbb{N}$ at heights $h_m\in\mathbb{N}$, where $(h_m)$ is strictly increasing, and equ…

Let ${\cal H}^{(p,s)}(n)$ be the family of vertex sets of subgraphs of $nK_2$ having $p$ edges and $s$ isolated vertices. Say that a family is $r$-EKR when its largest intersecting…

Let $G$ be a twin-free graph of order $n$, and let a locating-dominating set be a set of vertices that is both locating and dominating. Write $\gamma^{LD}(G)$ for the minimum size…

Let $X(\infty)$ be the limiting estimator produced by the memoryless iterative process on an interval graph of length $n$, and let $Z(\infty)$ be the benchmark estimator used in th…

Gaussian-profile conjecture. The coefficients $A_k$ approach a Gaussian profile centered at the midpoint, in the sense that