7 problems

Steingrímsson's conjecture. The generating functions of these statistics on ordered set partitions are given by either side of

For $n\geq 0$, define … where $S^o[n,k]$ are the ordered type $A$ $q$-Stirling polynomials. Palindromicity and sign-pattern conjecture. The polynomial $F_n(q)$ is palindromic after…

Let $S[n,k]$, $S_B[n,k]$, $c[n,k]$, and $c_B[n,k]$ denote the four families of type $A$ and type $B$ $q$-Stirling polynomials, and view each polynomial's coefficients as a probabil…

For a finite coefficient sequence $(a_0,\ldots,a_n)$, call it bottom heavy when $a_k\geq a_{n-k}$ for $k<n/2$. Let $S[n,k]$, $c[n,k]$, $S_B[n,k]$, and $c_B[n,k]$ be the type $A$ an…

For each pair of nonnegative integers $n$ and $k$, let $S_B[n,k]$ and $c_B[n,k]$ be the type $B$ $q$-Stirling polynomials. A coefficient sequence is parity log-concave when its eve…

Let $\operatorname{SRB}_n$ be the type $B$ super coinvariant algebra, defined by … Here $S_B^o[n,k]$ denotes the ordered type $B$ $q$-Stirling number. Swanson–Wallach conjecture. W…

The type $A$ superdiagonal coinvariant algebra is a triply graded algebra whose Hilbert series records the ordered $q$-Stirling numbers $S^o[n,k]$. Zabrocki's conjecture. The tri-g…