Geodesic
Combinatorial Laplacians of matroid complexes
Kook, W.1, 2 ; Reiner, V.1 ; Stanton, D.1
1 School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
2 Department of Mathematics, The George Washington University, Washington DC 20052
Journal of the American Mathematical Society, Tome 13 (2000) no. 1, pp. 129-148

Voir la notice de l'article provenant de la source American Mathematical Society

We combinatorially interpret the spectra of discrete Laplace operators from the boundary maps in the simplicial complex of independent sets of a matroid. The interpretation follows from a surprising orthogonal decomposition of the simplicial chain groups. This decomposition is in general finer than the spectral decomposition. As a consequence, the spectra are integral. One corollary to our combinatorial interpretation may be paraphrased as stating that one can “hear" the characteristic polynomial of a matroid.
DOI : 10.1090/S0894-0347-99-00316-1

Kook, W. 1, 2 ; Reiner, V. 1 ; Stanton, D. 1

1 School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
2 Department of Mathematics, The George Washington University, Washington DC 20052 
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Kook, W.; Reiner, V.; Stanton, D. Combinatorial Laplacians of matroid complexes. Journal of the American Mathematical Society, Tome 13 (2000) no. 1, pp. 129-148. doi: 10.1090/S0894-0347-99-00316-1

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