Abstract
Let M be a matroid on E, representable over a field of characteristic zero. We show that h-vectors of the following simplicial complexes are log-concave:. 1.The matroid complex of independent subsets of E.2.The broken circuit complex of M relative to an ordering of E. The first implies a conjecture of Colbourn on the reliability polynomial of a graph, and the second implies a conjecture of Hoggar on the chromatic polynomial of a graph. The proof is based on the geometric formula for the characteristic polynomial of Denham, Garrousian, and Schulze.
Original language | English (US) |
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Pages (from-to) | 49-59 |
Number of pages | 11 |
Journal | Advances in Mathematics |
Volume | 270 |
DOIs | |
State | Published - Jan 2 2015 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Characteristic polynomial
- F-Vector
- H-Vector
- Hyperplane arrangement
- Log-concavity
- Matroid