5 problems

Let $f^\sharp_{n,k}(w)$ and $F_n^\sharp(x,w)=\sum_{k=0}^n f^\sharp_{n,k}(w)x^k$ be as above. A polynomial sequence is coefficientwise Hankel-totally positive when all minors of its…

Let $f^\sharp_{n,k}(w)$ be the entries of the exponential Riordan array with generating function $G(t)=(e^{wT(t)}-1)/w$, where $T(t)$) is the tree function, and define…

For $n,k\geq 0$, let $P_{n,k}(a,b)$ be the Schl"afli--Gessel--Seo forest polynomials, let $P_n(x;a,b)=\sum_{k=0}^n P_{n,k}(a,b)x^k$, and let $P_n(a,b)=P_{n,1}(a,b)$. A polynomial m…

Forest-Wilf implication conjecture. If $S$ and $S'$ are forest-Wilf equivalent, then $S$ and $S'$ are Wilf equivalent with respect to pattern avoidance in permutations.

Forest-Wilf equivalence conjecture. The following three equivalences hold: