Higher matrix-tree theorems

2011/09/29 by Yurii Burman, Burman, Yurii, Andrey Ploskonosov +3
Computer Science · Mathematics · #15A15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #math.CO #msc:15A15

paper · pdf · doi:10.48550/arxiv.1109.6625

10 pages, no figures

arxiv created 2011/09/29 · openalex publication_date 2011/09/29 · arxiv updated 2011/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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