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Peter Keevash (Queen Mary London)
Thursday 14 May 2009, 14:30-15:30
Shadows and intersections: stability and new proofs
- đ¤ Speaker: Peter Keevash (Queen Mary London)
- đ Date & Time: Thursday 14 May 2009, 14:30 - 15:30
- đ Venue: MR12
Abstract
We give a short new proof of a version of the Kruskal-Katona theorem due to Lov\’asz. Our method can be extended to a stability result, describing the approximate structure of configurations that are close to being extremal, which answers a question of Mubayi. This in turn leads to another combinatorial proof of a stability theorem for intersecting families, which was originally obtained by Friedgut using spectral techniques and then sharpened by Keevash and Mubayi by means of a purely combinatorial result of Frankl. We also give an algebraic perspective on these problems, giving yet another proof of intersection stability that relies on expansion of a certain Cayley graph of the symmetric group, and an algebraic generalisation of Lov\’asz’s theorem that answers a question of Frankl and Tokushige.
Series This talk is part of the Combinatorics Seminar series.
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