5 problems

Let $C_k$ denote the $k$th Catalan number, let $\operatorname{Nar}_{k}(t)$ denote the Narayana polynomial, and define … Let $W_{n,k}^{+}(t)$ and $W_{n,k}^{-}(t)$ be the symmetric-d…

Let $W_{n,k}(t)$ be the polynomials considered in the paper. A finite sequence of real-rooted polynomials is Sturm-unimodal if it increases by interlacing up to one index and then…

The Narayana number $N(n,k)$ counts Dyck paths of length $2n$ with exactly $k$ peaks, and the Narayana polynomials are $N_n(q)=\sum_{k=0}^{n}N(n,k)q^k$. A sequence of polynomials i…

Conjecture 7.6. The sixth Hankel determinant satisfies

Let $\mathsf{F}_t$ be the parameterized series, let $\mathsf{F}_{n,t}$ be its homogeneous component of degree $n$, let $\operatorname{\mathbf{ca}}_{n,t}$ be the corresponding $t$-N…