An EKR-theorem for finite buildings of type \(D_{\ell }\)

  • Ferdinand Ihringer
  • Klaus Metsch
  • Bernhard Mühlherr


We define optimal EKR-sets in finite buildings. This definition is motivated by various contributions on optimal EKR-sets in finite projective spaces and polar spaces. Our main result is the classification of optimal EKR-sets of type \(\{ \ell , \ell -1\}\) in finite building of type \(D_{\ell }\) with \(\ell \) even. As it is the case for most of the known optimal EKR-sets in finite buildings, our EKR-sets have a natural center. This provides some evidence that the EKR-problem for finite buildings and Tits center conjecture are closely related.


EKR-sets Polar spaces Finite buildings 

Mathematics Subject Classification

05C35 51A50 51E24 



We would like to thank the anonymous referee for reading our manuscript very carefully.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Einstein Institute of MathematicsThe Hebrew University of JerusalemGivat Ram, JerusalemIsrael
  2. 2.Mathematisches InstitutJustus-Liebig-UniversitätGiessenGermany

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