Induced equators in flag spheres

Maria Chudnovsky; Eran Nevo

doi:10.1016/j.jcta.2020.105283

Induced equators in flag spheres

Maria Chudnovsky, Eran Nevo

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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)h_i(Δ)≥(d−i+1)h_i−1(Δ)+(i+1)h_i+1(Δ) for all 0≤i≤d.

Original language	English (US)
Article number	105283
Journal	Journal of Combinatorial Theory. Series A
Volume	176
DOIs	https://doi.org/10.1016/j.jcta.2020.105283
State	Published - 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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10.1016/j.jcta.2020.105283

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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",

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year = "2020",

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doi = "10.1016/j.jcta.2020.105283",

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AU - Chudnovsky, Maria

AU - Nevo, Eran

PY - 2020/11

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N2 - 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.

AB - 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.

KW - Clique complex

KW - Flag polytope

KW - Flag sphere

KW - Gal's conjecture

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JO - Journal of Combinatorial Theory. Series A

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M1 - 105283

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Induced equators in flag spheres

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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