Geodesic
A colourful path to matrix-tree theorems
Kassel, Adrien1 ; Lévy, Thierry2
1 CNRS, UMPA École Normale Supérieure de Lyon 46, allée d’Italie F-69007 Lyon, France
2 LPSM Sorbonne Université 4, place Jussieu F-75005 Paris, France
Algebraic Combinatorics, Tome 3 (2020) no. 2, pp. 471-482.

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In this short note, we revisit Zeilberger’s proof of the classical matrix-tree theorem and give a unified concise proof of variants of this theorem, some known and some new.

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DOI : 10.5802/alco.100
Classification : 05C30, 05C22, 15A15
Mots-clés : matrix-tree theorem, graph, forests, cycles, Laplacian, determinant, Q-determinant, holonomy, ordered products, simplicial complexes, pseudoforests, circular and bicircular matroids

Kassel, Adrien 1 ; Lévy, Thierry 2

1 CNRS, UMPA École Normale Supérieure de Lyon 46, allée d’Italie F-69007 Lyon, France
2 LPSM Sorbonne Université 4, place Jussieu F-75005 Paris, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Kassel, Adrien; Lévy, Thierry. A colourful path to matrix-tree theorems. Algebraic Combinatorics, Tome 3 (2020) no. 2, pp. 471-482. doi : 10.5802/alco.100. https://geodesic-test.mathdoc.fr/articles/10.5802/alco.100/

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  • Cimasoni, David; Kassel, Adrien Graph coverings and twisted operators, Algebraic Combinatorics, Volume 6 (2023) no. 1, pp. 75-94 | DOI:10.5802/alco.258 | Zbl:1511.05193
  • Kassel, Adrien; Lévy, Thierry Determinantal probability measures on Grassmannians, Annales de l'Institut Henri Poincaré D. Combinatorics, Physics and their Interactions, Volume 9 (2022) no. 4, pp. 659-732 | DOI:10.4171/aihpd/152 | Zbl:1511.60072
  • Kassel, Adrien; Lévy, Thierry Covariant Symanzik identities, Probability and Mathematical Physics, Volume 2 (2021) no. 3, pp. 419-475 | DOI:10.2140/pmp.2021.2.419 | Zbl:1483.60112

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