On q-analogues and stability theorems

Abstract

In this survey recent results about q -analogues of some classical theorems in extremal set theory are collected. They are related to determining the chromatic number of the q -analogues of Kneser graphs. For the proof one needs results on the number of 0-secant subspaces of point sets, so in the second part of the paper recent results on the structure of point sets having few 0-secant subspaces are discussed. Our attention is focussed on the planar case, where various stability results are given.