2 problems

Let $\mathcal{C}$ be an infinite subclass of self-avoiding walks in an upper half-plane, with starting point on the surface. For $\omega\in\mathcal{C}$, let $h(\omega)$ be the maxi…

Let $W(z;1,0;a)$ be the generating function for prudent loops, with step variable $z$ and surface fugacity $a>0$. Let $z_{1}^{\ell}\approx 0.412095$ denote a root of … and let…