Shadows and intersections: stability and new proofs
| dc.creator | Keevash, Peter | |
| dc.date | 2008-06-12 | |
| dc.date.accessioned | 2026-07-07T09:44:09Z | |
| dc.date.available | 2026-07-07T09:44:09Z | |
| dc.description | 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. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/0806.2023 | |
| dc.identifier | http://arxiv.org/abs/0806.2023 | |
| dc.identifier | Adv. Math. 218 (2008), 1685--1703 | |
| dc.identifier | doi:10.1016/j.aim.2008.03.023 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162770 | |
| dc.subject | Combinatorics | |
| dc.subject | 05D05 | |
| dc.title | Shadows and intersections: stability and new proofs | |
| dc.type | text |