Face enumeration on flag complexes and flag spheres
Hailun Zheng
TL;DR
This paper surveys recent advances and open problems in the face enumeration of flag complexes and flag spheres, focusing on face vector characterizations and conjectures like Charney-Davis and Gal's conjecture.
Contribution
It provides a comprehensive overview of recent results, conjectures, and open problems related to face enumeration in flag complexes and flag spheres.
Findings
Discussion of face vector characterizations
Analysis of lower-bound conjectures including Charney-Davis and Gal's conjecture
Examination of the upper bound conjecture for flag spheres
Abstract
We give a survey on the recent results and problems on the face enumeration of flag complexes and flag simplicial spheres, with an emphasis on the characterization of face vectors of flag complexes, several lower-bound type of conjectures including the Charney-Davis conjecture and Gal's conjecture, and the upper bound conjecture for flag spheres and pseudomanifolds.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Topological and Geometric Data Analysis