## Combinatorial Laplacians of matroid complexes

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- by W. Kook, V. Reiner and D. Stanton PDF
- J. Amer. Math. Soc.
**13**(2000), 129-148 Request permission

## 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.## References

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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
- MR Author ID: 262157
- Email: reiner@math.umn.edu
**D. Stanton**- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- Email: stanton@math.umn.edu
- Received by editor(s): July 16, 1997
- Received by editor(s) in revised form: June 30, 1999
- Published electronically: 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 1999 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**13**(2000), 129-148 - MSC (2000): Primary 05B35
- DOI: https://doi.org/10.1090/S0894-0347-99-00316-1
- MathSciNet review: 1697094