Relaxations of the matroid axioms I: Independence, exchange and circuits

Research output: Contribution to journalConference article

1 Scopus citations

Abstract

Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial complexes. The resulting classes retain some of the matroid properties and allow us to classify matroid properties according to the relevant axioms needed to prove them. We illustrate this by discussing Tutte polynomials. Furthermore, we extend a conjecture of Stanley on h-vectors and provide evidence to show that the extension is better suited than matroids to study the conjecture.

Original languageEnglish (US)
Pages (from-to)1075-1086
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - 2016
Externally publishedYes
Event28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016 - Vancouver, Canada
Duration: Jul 4 2016Jul 8 2016

Keywords

  • H-vectors
  • Matroid
  • Shifted Complex
  • Tutte polynomial

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Discrete Mathematics and Combinatorics

Fingerprint Dive into the research topics of 'Relaxations of the matroid axioms I: Independence, exchange and circuits'. Together they form a unique fingerprint.

  • Cite this