Higher matrix-tree theorems
Yurii Burman, Andrey Ploskonosov, Anastasia Trofimova
TL;DR
This paper generalizes classical matrix-tree theorems by calculating determinants of sums of reflections and their commutators, extending known combinatorial results to broader algebraic contexts.
Contribution
It introduces new determinant formulas for sums of reflections and their commutators, generalizing Kirchhoff's and matrix-3-hypertree theorems.
Findings
Derived determinant formulas for sums of reflections.
Extended classical matrix-tree theorems to new algebraic structures.
Provided algebraic generalizations of combinatorial theorems.
Abstract
We calculate determinants of weighted sums of reflections and of (nested) commutators of reflections. The results obtained generalize the Kirchhoff's matrix-tree theorem and the matrix-3-hypertree theorem by G.\,Massbaum and A.\,Vaintrob.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Matrix Theory and Algorithms · Graph theory and applications