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.

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 
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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. http://www.numdam.org/articles/10.5802/alco.100/

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