11 problems

Let $\mathcal{A}$ be a real hyperplane arrangement, with magnitude homology groups $MH_{k,\ell}(\mathcal{A})$ and intersection lattice $L(\mathcal{A})$. Magnitude homology conjectu…

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

Let $G$ be a graph and let $v\in G$ be a vertex having the highest centrality under magnitude homology centrality. The top node axiom is the condition that adding any edge incident…

Let the Eulerian magnitude homology centrality be defined on graphs, and let the density axiom mean the condition that, for the relevant graph family, the centrality comparison is…

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…

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

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

Let $W_n$ be the wheel graph on $n$ vertices, and write $V(W_n)$ and $E(W_n)$ for its vertex and edge sets. Let $\operatorname{MH}_{k,k}(W_n)$ denote its magnitude homology on the…

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…