2019/08/23 by Chudnovsky, Maria, Nevo, Eran
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1908.08727
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.