ALGEBRAIC COMBINATORICS

no. 2

A colourful path to matrix-tree theorems
Algebraic Combinatorics, Volume 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.

Received: 2019-03-13
Revised: 2019-09-10
Accepted: 2019-10-15
Published online: 2020-04-01
DOI: https://doi.org/10.5802/alco.100
Classification: 05C30,  05C22,  15A15
Keywords: matrix-tree theorem, graph, forests, cycles, Laplacian, determinant, Q-determinant, holonomy, ordered products, simplicial complexes, pseudoforests, circular and bicircular matroids 
@article{ALCO_2020__3_2_471_0,
     author = {Kassel, Adrien and L\'evy, Thierry},
     title = {A colourful path to matrix-tree theorems},
     journal = {Algebraic Combinatorics},
     pages = {471--482},
     publisher = {MathOA foundation},
     volume = {3},
     number = {2},
     year = {2020},
     doi = {10.5802/alco.100},
     language = {en},
     url = {alco.centre-mersenne.org/item/ALCO_2020__3_2_471_0/}
}
Kassel, Adrien; Lévy, Thierry. A colourful path to matrix-tree theorems. Algebraic Combinatorics, Volume 3 (2020) no. 2, pp. 471-482. doi : 10.5802/alco.100. https://alco.centre-mersenne.org/item/ALCO_2020__3_2_471_0/

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