Shadows and intersections: stability and new proofs

Details Shadows and intersections: stability and new proofs Shadows and intersections: stability and new proofs

2008-06-12

arxiv.org/abs/0806.2023v1

Adv. Math. 218 (2008), 1685--1703

Mathematics

Combinatorics

18 pages

Scientific paper

10.1016/j.aim.2008.03.023

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.

Affiliated with

Also associated with

No associations

Rating

Shadows and intersections: stability and new proofs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Shadows and intersections: stability and new proofs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Shadows and intersections: stability and new proofs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-690734