6 problems

Let $\textbf P$ be a differential poset, meaning a graded locally finite poset with a unique least element whose up- and down-degree operators satisfy Stanley's differential-poset…

Unbounded rank-gap conjecture. In any differential poset,

Let $A$ be an abelian group of order $r$, let $\mathfrak{S}$ denote the tower of symmetric groups, and consider the differential tower of groups $A\wr\mathfrak{S}$. For $k\leq n$,…

Let $P$ be a differential poset, let $p_n$ denote the size of its rank-$n$ set, and let $U_{n-1}D_n$ be the composite of the down operator $D_n$ from rank $n$ to rank $n-1$ with th…

Miller–Reiner conjecture. For any differential poset $P$ and any $n\geq 0$, the matrix

Let $r$ be a positive integer, let $P$ be an $r$-differential poset, let $P_n$ denote its $n$th rank, and write $p_n:=|P_n|$ for the rank cardinalities. Stanley's conjecture. An…