@article{752f6bd9f9234c01803b96bc4797a87a,
title = "Induced equators in flag spheres",
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.",
keywords = "Clique complex, Flag polytope, Flag sphere, Gal's conjecture",
author = "Maria Chudnovsky and Eran Nevo",
note = "Funding Information: M. Chudnovsky was partially supported by NSF grants DMS-1763817 and by ERC advanced grant 320924. This material is based upon work supported in part by the U.S. Army Research Office under grant number W911NF-16-1-0404. E. Nevo was partially supported by the Israel Science Foundation grant ISF-1695/15, by ISF-BSF joint grant 2016288, and by ISF-NRF Singapore joint research program grant 2528/16. Funding Information: M. Chudnovsky was partially supported by NSF grants DMS-1763817 and by ERC advanced grant 320924 . This material is based upon work supported in part by the U.S. Army Research Office under grant number W911NF-16-1-0404 . E. Nevo was partially supported by the Israel Science Foundation grant ISF-1695/15 , by ISF-BSF joint grant 2016288 , and by ISF-NRF Singapore joint research program grant 2528/16 . Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",
year = "2020",
month = nov,
doi = "10.1016/j.jcta.2020.105283",
language = "English (US)",
volume = "176",
journal = "Journal of Combinatorial Theory. Series A",
issn = "0097-3165",
publisher = "Academic Press Inc.",
}