Induced equators in flag spheres

Maria Chudnovsky, Eran Nevo

Research output: Contribution to journalArticle

Abstract

We propose a combinatorial approach to the following strengthening of Gal's conjecture: γ(Δ)≥γ(E) coefficientwise, where Δ is a flag homology sphere and E⊆Δ an induced homology sphere of codimension 1. We provide partial evidence in favor of this approach, and prove a nontrivial nonlinear inequality that follows from the above conjecture, for boundary complexes of flag d-polytopes: h1(Δ)hi(Δ)≥(d−i+1)hi−1(Δ)+(i+1)hi+1(Δ) for all 0≤i≤d.

Original languageEnglish (US)
Article number105283
JournalJournal of Combinatorial Theory. Series A
Volume176
DOIs
StatePublished - Nov 2020

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Keywords

  • Clique complex
  • Flag polytope
  • Flag sphere
  • Gal's conjecture

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