A colourful path to matrix-tree theorems

DOI10.5802/alco.100zbMath1436.05049arXiv1903.02491OpenAlexW3105396499MaRDI QIDQ1985361

Thierry Lévy, Adrien Kassel

Publication date: 7 April 2020

Published in: Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.02491

zbMATH Keywords

cyclessimplicial complexesholonomydeterminantLaplacianforestsmatrix-tree theorembicircular matroidsordered productscircular matroidspseudoforestsQ-determinant

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Enumeration in graph theory (05C30) Signed and weighted graphs (05C22) Combinatorial aspects of simplicial complexes (05E45)

Related Items (3)

Covariant Symanzik identities ⋮ Determinantal probability measures on Grassmannians ⋮ Graph coverings and twisted operators

Cites Work

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• Directed rooted forests in higher dimension
• Spanning forests and the vector bundle Laplacian
• Enumeration of \({\mathbb{Q}}\)-acyclic simplicial complexes
• A combinatorial approach to matrix algebra
• Signed graphs
• Counting colorful multi-dimensional trees
• Determinants of Laplacians on graphs
• Covariant Symanzik identities
• Learning about critical phenomena from scribbles and sandpiles
• Simplicial and cellular trees
• RANDOM COMPLEXES AND ℓ²-BETTI NUMBERS
• Simplicial matrix-tree theorems
• A Combinatorial Proof of the All Minors Matrix Tree Theorem

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