Shadows and intersections: Stability and new proofs |
| |
Authors: | Peter Keevash |
| |
Affiliation: | School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK |
| |
Abstract: | We give a short new proof of a version of the Kruskal-Katona theorem due to Lovász. 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 Lovász's theorem that answers a question of Frankl and Tokushige. |
| |
Keywords: | Set systems Shadows Intersections Stability |
本文献已被 ScienceDirect 等数据库收录! |
|