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Combinatorial Laplacians of matroid complexes
Author(s):
W.
Kook;
V.
Reiner;
D.
Stanton
Journal:
J. Amer. Math. Soc.
13
(2000),
129-148.
MSC (2000):
Primary 05B35
Posted:
September 13, 1999
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Abstract:
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.
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Additional Information:
W.
Kook
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Address at time of publication:
Department of Mathematics, The George Washington University, Washington DC 20052
Email:
kook@math.umn.edu, andrewk@gwu.edu
V.
Reiner
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email:
reiner@math.umn.edu
D.
Stanton
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email:
stanton@math.umn.edu
DOI:
10.1090/S0894-0347-99-00316-1
PII:
S 0894-0347(99)00316-1
Keywords:
Matroid,
matroid complex,
Laplacian,
internal activity,
external activity
Received by editor(s):
July 16, 1997
Received by editor(s) in revised form:
June 30, 1999
Posted:
September 13, 1999
Additional Notes:
The second author was supported by Sloan Foundation and University of Minnesota McKnight Land Grant Fellowships. The third author was supported by NSF grant DMS-9400510.
Copyright of article:
Copyright
1999,
American Mathematical Society
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