2 problems

Sokal's functional-digraph conjecture. The following assertions hold: (i) $[\psi_{n,k}]_{n,k}$ is totally positive; (ii) $(\bm{\psi}_n(y))_{n\geq0}$ is coefficientwise Hankel-total…

Let $\Psi_n(x,y)$ be the generating polynomial for functional digraphs on $[n]$, with weight $x$ for each cyclic vertex and weight $y$ for each component. Define…