4 problems

Let $p_{i,j}$ be the undirected circuits constructed in the preceding result, representing the relevant homology classes in the weighted digraph filtration. Simplicity conjecture.…

Let $A\in\mathbb{R}_+^{n\times n}$ be a weighted matrix, and let $T_k(A)$ denote the transient of its $k$th row or column when that row or column is critical. Let…

Let $D$ be a weighted loopless digraph with $n\geq 2$ vertices. For each vertex $v\in V(D)$, write $d^{w+}(v)$ for its weighted outdegree, and write $w(C)$ for the total weight of…

A weighted digraph is a digraph whose arcs have nonnegative weights; it is loopless if it has no loops. For a vertex $v$, let $d^{w+}(v)$ be its weighted outdegree, the sum of the…