How to construct a flag complex with a given face vector

TL;DR

This paper presents a method for constructing flag complexes with specified face vectors and extends it to create vertex-decomposable, Cohen-Macaulay flag complexes with given h-vectors, advancing combinatorial topology techniques.

Contribution

Introduces a versatile method for constructing flag complexes with predetermined face vectors and extends it to generate vertex-decomposable complexes with specified h-vectors.

Findings

Method often successfully constructs flag complexes with given face vectors.

Can adapt the method to produce vertex-decomposable, Cohen-Macaulay flag complexes.

Provides a systematic approach for targeted complex construction.

Abstract

A method that often works for constructing a flag complex with a specified face vector is given. This method can also be adapted to construct a vertex-decomposable (and hence Cohen-Macaulay) flag complex with a specified h-vector.