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

Abstract

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.

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Acknowledgements

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

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Correspondence to Ferdinand Ihringer.

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Ihringer, F., Metsch, K. & Mühlherr, B. An EKR-theorem for finite buildings of type \(D_{\ell }\) . J Algebr Comb 47, 529–541 (2018). https://doi.org/10.1007/s10801-017-0784-0

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Keywords

  • EKR-sets
  • Polar spaces
  • Finite buildings

Mathematics Subject Classification

  • 05C35
  • 51A50
  • 51E24