9 problems

Let $D$ be a directed graph, and let $\operatorname{\mathcal{O}}(D)$ denote its ornamentation lattice. Polytopal realization conjecture. For any directed graph $D$, the ornamentati…

Bóna–Ju–Ann conjecture. If $k=2\ell$, then

Ju's conjecture. The polynomial in the numerator of this Ehrhart series is symmetric, also known as palindromic.

Higashitani–Kummer–Michałek conjecture. (i) For any complete multipartite graph $K_{a_1,\dots,a_k}$, the roots of $E_{a_1,\dots,a_k}$ lie on $\operatorname{CL}$. (ii) If…

Let $G$ be a connected graph with $n\geq 3$ vertices. Let ${\mathcal P}_G$ be its symmetric edge polytope, and let $N({\mathcal P}_G)$ denote the number of its facets. A $1$-sum of…

Ohsugi–Tsuchiya conjecture. For every $i\geq 0$,

Polytope characterization conjecture. There is a polytope $P$ whose vertices are labelled by the edges of $G$ and whose faces are in bijection with the induced subgraphs of $G$ hav…

Let ${\mathcal A}_G$ be a symmetric edge polytope of type A, and let $h^*({\mathcal A}_G,x)$ denote its $h^*$-polynomial. Type A symmetric edge-polytope conjecture. The $h^*$-polyn…

Let $G$ be a complete $k$-partite graph of type $(a_1,\dots,a_k)$, and let $H_{a_1,\dots,a_k}$ denote its Ehrhart polynomial. Complete multipartite Ehrhart conjecture. The polynomi…