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Discrete Math

Large Erdos-Ko-Rado Sets in Vector and Polar Spaces

Ferdinand Ihringer: University of Regina

Location:  Hill 705
Date & time: Monday, 06 March 2017 at 2:00PM - 2:11PM

An Erdos-Ko-Rado set (EKR set) Y of { 1, ..., n } is a family of k-sets, which pairwise intersect non-trivially. A non-trivial problem is to provide tight upper bounds on Y and classify all examples, which obtain that bound. Erdos, Ko and Rado proved |Y| = 2k. Equality holds for n = 2k+1 if and only if Y is the family of all k-sets, which contain one fixed element.

If one considers { 1, ..., n } as the vector space over the field with 1 element, then it is natural to generalize the concept of EKR sets to vector spaces over finite fields. Here an EKR set of a vector space of dimension n is a family of k-spaces, which pairwise meet non-trivially. If we equip a vector space over a finite field of order q with a reflexive, non-degenerate sesquilinear form, then the subspaces that vanish on this form constitute a highly symmetric geometric structure, a polar space.

The talk will introduce the audience to some aspects of EKR sets in vector and polar spaces. In particular we will elaborate on classification results that use spectral techniques.

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