4 problems

For each positive integer $n$, let $P_{n,n}$ be the $n\times n$ grid polygon, and choose a random unimodular triangulation of $P_{n,n}$. A triangulation is irregular if it is not r…

Let $P_{m,n}$ be the $m\times n$ grid polygon, and consider its unimodular triangulations. A triangulation is regular if it is induced by a lifting function, and non-regular otherw…

Let $f(m,n)$ denote the number of lattice triangulations of a rectangle of width $m$ and length $n$, and let $c_m$ be the corresponding exponential growth constant. Asymptotic conj…

Let $\Omega(n,k)$ be the state space of lattice triangulations of an $n\times k$ rectangle, with parameter $\lambda>0$ and Glauber dynamics whose mixing time is … The parameter ran…