REVIEW
A Combinatorial Formula for Principal Minors of a Matrix with Tree-metric Exponents and Its Applications
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
A Combinatorial Formula for Principal Minors of a Matrix with Tree-metric Exponents and Its Applications
read the original abstract
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 of principal minors of the matrix $(t^{d_{ij}})$, and its applications to tropical geometry, study of multivariate stable polynomials, and representation of valuated matroids. We also give an analogous formula for a skew-symmetric matrix associated with $T$.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.