9 problems

Milner–Sauer conjecture. The poset $P$ must contain an antichain of size $\kappa$.

Let $S$ be a connected partially ordered set. A partially ordered set is $P$-faithful when it satisfies the notion of $P$-faithfulness used in the paper, and a uniform wattle is a…

Let $P$ be a finite partially ordered set, and consider the two notions of monotonicity for continuous-time Markov processes on $P$ studied by Dai Pra et al. An acyclic extension i…

RZ-X conjecture. The partially ordered sets are isomorphic:

Let $S$ be a connected poset with no acyclic extension. Conjecture. Monotonicity equivalence holds for $S$ if and only if the conditions stated in the source are satisfied. The pap…

For a positive integer $k$, let $\mathbf{k}+\mathbf{k}$ be the poset consisting of two disjoint $k$-element chains with no comparabilities between distinct chains. Let…

For positive integers $k$ and $w$, let $f(k,w)$ be the maximum size of a subset of $\mathbb{Z}^w$ in which every two vectors are $1$-crossing but no two vectors are $k$-crossing. F…

Let $T$ and $T'$ be unlabelled trees, considered up to isomorphism, with $n$ vertices. For a tree $T$, let $\mathcal{B}(T)$ denote its graph building set and let…

Let a finite partially ordered set be presented to a selector in uniformly random order. A strategy observes the items online and may accept an item, with the objective of acceptin…