A Combinatorial Formula for Principal Minors of a Matrix with Tree-metric Exponents and Its Applications

Hiroshi Hirai, Akihiro Yabe

Let $T$ be a tree with a vertex set $\{1,2,\dots ,N\}$. Denote by $d_{ij}$ the distance between vertices $i$ and $j$. In this paper, we present an explicit combinatorial formula…