Flag vectors

Original · EN

This paper defines for each object X that can be constructed out of a finite number of vertices and cells a vector fX lying in a finite dimensional vector space. This is the flag vector of X. It is hoped that the quantum topological invariants of a manifold M can be expressed as linear functions of the flag vector of the i-graph that arises from any suitable triangulation T of M. Flag vectors are also defined for finite groups and more generally for n-ary relations. Some problems, and suggested connections with other constructions, particularly that of the associahedron and so on, conclude the presentation.