2024/10/10 by Soohyun Park, Park, Soohyun
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2410.08139
openalex publication_date 2024/10/10 · openalex created_date 2024/10/13 · openalex updated_date 2026/07/28
We show that there are f-vectors of balanced simplicial complexes giving a source of simplicial complexes exhibiting a Boolean decomposition similar to a geometric Lefschetz decomposition. The objects we are working with are h-vectors of flag spheres and balanced simplicial complexes whose f-vectors are equal to them. This builds on work of Nevo--Petersen--Tenner on a conjecture of Nevo--Petersen that the gamma vector of an odd-dimensional flag sphere is the f-vector of a balanced simplicial complex (which was shown for barycentric subdivisions by Nevo--Petersen--Tenner). We can connect our decomposition to positivity questions on reciprocal/palindromic polynomials associated to flag spheres and geometric questions motivating them. In addition, we note that the degrees in the Lefschetz-like decomposition are not halved unlike the usual h-vector setting.