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Journal of Geometry

, Volume 101, Issue 1–2, pp 31–50 | Cite as

On q-analogues and stability theorems

  • Aart Blokhuis
  • Andries BrouwerEmail author
  • Tamás Szőnyi
  • Zsuzsa Weiner
Open Access
Article

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.

Mathematics Subject Classification (2010)

05D05 05B25 

Keywords

q-analogues Erdős–Ko–Rado theorem q-Kneser graph chromatic number blocking set stability results 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Aart Blokhuis
    • 1
  • Andries Brouwer
    • 1
    Email author
  • Tamás Szőnyi
    • 2
    • 3
  • Zsuzsa Weiner
    • 2
    • 4
  1. 1.Department of MathematicsEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Department of Computer ScienceEötvös Loránd UniversityBudapestHungary
  3. 3.Computer and Automation Research Institute of the Hungarian Academy of SciencesBudapestHungary
  4. 4.Prezi.comBudapestHungary

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