5 problems

For each $n\in\mathbb{N}$, let $\mathcal{L}(n)$ be the set of Latin squares of order $n$ using the symbols $[n]=\{1,2,\ldots,n\}$, and let $L_n\in\mathcal{L}(n)$ be chosen uniforml…

Infinite noodle component conjecture. The component $C_0$ is finite almost surely, and the probability that it has size at least $k$ satisfies

Let a Steiner triple system of order $n$ be a $3$-uniform hypergraph on $n$ vertices in which every pair lies in exactly one edge, and let a perfect matching be a set of $n/3$ pair…

A meandric system of size $n$ is a collection of non-crossing loops intersecting the horizontal axis exactly at the points $0,\ldots,2n-1$, up to continuous deformation fixing the…

Let $P$ be a finite connected poset. Let $e(P)$ and $e^*(P)$ be the consecutive-level parameters, and let $d(P)$ and $d^*(P)$ be the minimum ratios defined over connected subposets…