5 problems

Let $P$ be a finite poset. A local realizer of $P$ is a family of partial linear extensions whose frequency is the maximum number of partial linear extensions in which any element…

Asymptotic local dimension conjecture for powers of chains. There exists a universal constant $c$ such that, for any $t\in\operatorname{\mathbb{N}}$, as $n\to\infty$,

Weak Boolean lattice local dimension conjecture.

Let $\mathcal{P}=(P,\leq)$ be a poset with $|P|\geq 3$, and let $\operatorname{ldim}(\mathcal{P})$ denote its local dimension. For $x,y\in P$, write $\mathcal{P}-\{x,y\}$ for the p…

Local-dimension conjecture. With the exception of weak Perron parameters $\beta$, the only value of the local dimension larger than one for a Bernoulli convolution is