Flag Folding

Flag Variety

1.1. QCoh on a stack. We know that QCoh forms a stack, i.e., sheaf of groupoids, over Schfpqc(S) for any scheme S. Thus if we have an fpqc sheaf of groupoids X over S, we can define QCoh(X ) as maps of sheaves X → QCoh on Schfpqc(S). By 2-Yoneda, this definition agrees with the usual notion of quasicoherent sheaves if X is a scheme. For various other (usually equivalent) definitions in the case...

Flag algebras

Asymptotic extremal combinatorics deals with questions that in the language of model theory can be re-stated as follows. For finite models M, N of an universal theory without constants and function symbols (like graphs, digraphs or hypergraphs), let p(M, N) be the probability that a randomly chosen sub-model of N with |M | elements is isomorphic to M . Which asymptotic relations exist between t...

Flag Vectors

This paper deenes for each object X that can be constructed out of a nite number of vertices and cells a vector fX lying in a nite dimensional vector space. This is the ag vector of X. It is hoped that the quantum topological invariants of a manifold M can be expressed as linear functions of the ag vector of the i-graph that arises from any suitable triangulation T of M. Flag vectors are also d...

Flag Matroids

The affine flag variety