A colourful path to matrix-tree theorems

Adrien Kassel (1) , Thierry Lévy (2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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.

Mots clés: matrix-tree theorem; forests; cycles; Laplacian; determinant; circular and bicircular matroids; simplicial complexes; holonomy; Q-determinant

Domaines: Combinatoire [math.CO]

Adrien Kassel, Thierry Lévy. A colourful path to matrix-tree theorems. Algebraic Combinatorics, 2020, 3 (2), pp.471-482. ⟨10.5802/alco.100⟩. ⟨hal-02059636v2⟩