7 problems

Path-tree recurrence conjecture. For $0\leq k\leq n$ and all $\ell\geq 0$,

Tree discriminant magnitude homology conjecture. For $k=3,4$,

Let $\mathcal{A}$ be a real hyperplane arrangement of rank $r$, let $n=\#\mathcal{A}$, and write its reduced magnitude as … Let $\mathcal{T}(\mathcal{A})$ denote the tope graph, le…

Linear growth conjecture. There exists a linear function $\varphi$ such that, whenever

Let $C_3$ and $C_4$ denote cycle graphs of lengths three and four, respectively. Form a graph by gluing any number of copies of $C_3$ along single edges to a single copy of $C_4$,…

Let $C_3$ and $C_4$ denote cycle graphs of lengths three and four, respectively. Form a graph by gluing two copies of $C_3$ along single edges to a single copy of $C_4$, and suppos…

Let $C_4$ denote a square cycle, and let $G^4_S$ be a square polyomino formed from $S$ copies of $C_4$. Write $V(G^4_S)$ and $E(G^4_S)$ for its vertex and edge sets, and let…