8 problems

Global chain decomposition conjecture. There exist collections of partitions $\mathcal{C}_{\mu}$, indexed by deficit partitions $\mu$, and a size-preserving involution…

Let $B_n$ be the Boolean algebra of all subsets of $[n]$, ordered by inclusion. A chain decomposition of $B_n$ has a type, namely the partition obtained by rearranging its chain si…

Let $F(\beta)$ be a fence and let $L(\beta)$ be its distributive lattice of lower order ideals. For a linear extension of $F(\beta)$, form the corresponding lexicographic chain dec…

Let $F(\beta)$ be a fence and let $L(\beta)$ be its distributive lattice of lower order ideals, with rank sequence governed by the alternatives in Theorem heavy. A saturated chain…

Upper-half dominance conjecture. If $s_1\geq\dots\geq s_M$ is a sequence of positive integers dominated by $\sigma_1',\dots,\sigma_M'$ and

Griggs's conjecture. If $s_1\geq\dots\geq s_M$ is a sequence of positive integers dominated by $\sigma_1,\dots,\sigma_M$ and

Uniform rank-symmetric chain conjecture. For every positive integer $h$ there exists a positive integer $N(h)$ such that, whenever $n>N(h)$ and $n$ is odd, the Boolean lattice…

Rank-symmetric chain conjecture. The Boolean lattice $2^{[n]}$ can be partitioned into $\binom{n}{\lfloor n/2\rfloor}$ rank-symmetric chains such that the size of any two chains di…