4 problems

Let $G$ be a finite graph, let $\boldsymbol{X}$ and $\boldsymbol{Y}$ denote the variables of its flat space wavefunction $\psi_G$, and let $\Omega_G$ be the canonical form of the c…

Let $G$ be a graph, let $\mathbb{C}_G$ be its cosmological polytope, and let $T$ be a triangulation of $\mathbb{C}_G$ arising from a good term order on $R_G$. For each simplex…

Let $P_k$, $P_\ell$, and $P_m$ be paths of lengths $k$, $\ell$, and $m$, respectively, and let $G$ be the graph obtained by identifying the three starting nodes and the three endin…

Let $G=(V,E)$ be a graph, and let $h^*(\mathbb{C}_G;z)$ denote the $h^*$-polynomial of its cosmological polytope. For polynomials with nonnegative coefficients, write $f\preceq g$…