Logarithmic concavity for morphisms of matroids

Christopher Eur, June Huh

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Morphisms of matroids are combinatorial abstractions of linear maps and graph homomorphisms. We introduce the notion of a basis for morphisms of matroids, and show that its generating function is strongly log-concave. As a consequence, we obtain a generalization of Mason's conjecture on the f-vectors of independent subsets of matroids to arbitrary morphisms of matroids. To establish this, we define multivariate Tutte polynomials of morphisms of matroids, and show that they are Lorentzian in the sense of [6] for sufficiently small positive parameters.

Original languageEnglish (US)
Article number107094
JournalAdvances in Mathematics
Volume367
DOIs
StatePublished - Jun 24 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Discrete convexity
  • Flag matroids
  • Log-concavity
  • Lorentzian polynomials
  • Matroids
  • Multivariate Tutte polynomials

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