H-Vectors of matroids and logarithmic concavity

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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 languageEnglish (US)
Pages (from-to)49-59
Number of pages11
JournalAdvances in Mathematics
Volume270
DOIs
StatePublished - Jan 2 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Characteristic polynomial
  • F-Vector
  • H-Vector
  • Hyperplane arrangement
  • Log-concavity
  • Matroid

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