Abstract
We show that the combinatorial Laplace operators associated to the boundary maps in a shifted simplicial complex have all integer spectra. We give a simple combinatorial interpretation for the spectra in terms of vertex degree sequences, generalizing a theorem of Merris for graphs. We also conjecture a majorization inequality for the spectra of these Laplace operators in an arbitrary simplicial complex, with equality achieved if and only if the complex is shifted. This generalizes a conjecture of Grone and Merris for graphs.
Original language | English (US) |
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Pages (from-to) | 4313-4344 |
Number of pages | 32 |
Journal | Transactions of the American Mathematical Society |
Volume | 354 |
Issue number | 11 |
DOIs | |
State | Published - Nov 2002 |
Keywords
- Laplace operator
- Laplacian
- Simplicial complex
- Spectra