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Theorems of Erdős-Ko-Rado type in geometrical settings

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Abstract

The original Erdős-Ko-Rado problem has inspired much research. It started as a study on sets of pairwise intersecting k-subsets in an n-set, then it gave rise to research on sets of pairwise non-trivially intersecting k-dimensional vector spaces in the vector space V (n, q) of dimension n over the finite field of order q, and then research on sets of pairwise non-trivially intersecting generators and planes in finite classical polar spaces. We summarize the main results on the Erdős-Ko-Rado problem in these three settings, mention the Erdős-Ko-Rado problem in other related settings, and mention open problems for future research.

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  1. Department of Mathematics, Krijgslaan 281-Building S22, 9000, Gent, Flanders, Belgium

    Maarten De Boeck & Leo Storme

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  1. Maarten De Boeck
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  2. Leo Storme
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Correspondence to Maarten De Boeck.

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De Boeck, M., Storme, L. Theorems of Erdős-Ko-Rado type in geometrical settings. Sci. China Math. 56, 1333–1348 (2013). https://doi.org/10.1007/s11425-013-4676-z

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