2014/03/27 by Christos A. Athanasiadis, Athanasiadis, Christos A. · 1 citation
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1403.7144
The enumerative theory of simplicial subdivisions (triangulations) of simplicial complexes was developed by Stanley in order to understand the effect of such subdivisions on the h-vector of a simplicial complex. A key role there is played by the concept of a local h-vector. This paper surveys some of the highlights of this theory and some recent developments, concerning subdivisions of flag homology spheres and their γ-vectors. Several interesting examples and open problems are discussed.