7 problems

For each $n$, consider the set of unlabelled isomorphism classes of trees with $n$ nodes. For a tree $T$, let $\mathcal{B}(T)$ be its graphical building set and let…

Let $G$ be the path on $n-2$ vertices, so that the graph associahedron $\mathcal{A}(G)$ is the classical associahedron, and let its chromatic number be denoted by…

Let $(P_k)_{k\geq 0}$ be a sequence of indecomposable simple polytopes whose classes freely generate a polynomial subring of $\mathfrak S$ closed under differentiation $d$. The sim…

Möbius-function conjecture. Even without the assumption that $L_G$ is a lattice, if the maximal tubings containing $\mathcal{X}$ form an interval $[\mathcal{Y},\mathcal{Z}]$, then

Let $G$ be a complete binary tree on $n$ vertices, and let $\mathcal{R}(G)$ be its rotation graph, whose vertices are the search trees on $G$ and whose edges correspond to single r…

A graphical nested complex is associated with a graph, and its primal and dual compatibility fans are the fans constructed from the corresponding compatibility data. Polytopality c…

Let $T$ and $T'$ be unlabelled trees, considered up to isomorphism, with $n$ vertices. For a tree $T$, let $\mathcal{B}(T)$ denote its graph building set and let…