Abstract
Erdős-Ko-Rado sets of planes in a projective or polar space are non-extendable sets of planes such that every two have a non-empty intersection. In this article we classify all Erdős-Ko-Rado sets of planes that generate at least a 6-dimensional space. For general dimension (projective space) or rank (polar space) we give a classification of the ten largest types of Erdős-Ko-Rado sets of planes. For some small cases we find a better, sometimes complete, classification.
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Acknowledgments
The author thanks Fr\(\acute{e}\)d\(\acute{e}\)ric Vanhove for his advice and for pointing out reference [6]. The author thanks Leo Storme for his careful reading. The research of this author is supported by FWO-Vlaanderen (Research Foundation—Flanders).
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This is one of several papers published in Designs, Codes and Cryptography comprising the special topic on “Finite Geometries: A special issue in honor of Frank De Clerck”.
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De Boeck, M. The largest Erdős-Ko-Rado sets of planes in finite projective and finite classical polar spaces. Des. Codes Cryptogr. 72, 77–117 (2014). https://doi.org/10.1007/s10623-013-9812-9
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DOI: https://doi.org/10.1007/s10623-013-9812-9