On q-analogues and stability theorems
Journal of Geometry, 2011•Springer
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.
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.
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.
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