COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

## Families with few k-chainsAdd to your list(s) Download to your calendar using vCal - Adam Zsolt Wagner (University of Illinois Urbana-Champaign)
- Thursday 23 February 2017, 14:30-15:30
- MR12.
If you have a question about this talk, please contact Andrew Thomason. A central theorem in combinatorics is Sperner’s Theorem, which determines the maximum size of a family in the Boolean lattice that does not contain a 2-chain. Erdos later extended this result and determined the largest family not containing a k-chain. Erdos and Katona and later Kleitman asked how many such chains must appear in families whose size is larger than the corresponding extremal result. This question was resolved for 2-chains by Kleitman in 1966, who showed that amongst families of size M in the Boolean lattice, the number of 2-chains is minimized by a family whose sets are taken as close to the middle layer as possible. He also conjectured that the same conclusion should hold for all k, not just 2. The best result on this question is due to Das, Gan and Sudakov who showed roughly that Kleitman’s conjecture holds for families whose size is at most the size of the k+1 middle layers of the Boolean lattice. Our main result is that for every fixed k and epsilon, if n is sufficiently large then Kleitman’s conjecture holds for families of size at most (1-epsilon)2^n, thereby establishing Kleitman’s conjecture asymptotically. Our proof is based on ideas of Kleitman and Das, Gan and Sudakov. Joint work with Jozsi Balogh. This talk is part of the Combinatorics Seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- Combinatorics Seminar
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Interested Talks
- MR12
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsCambridge Psychometrics Centre Seminars Humanitarian Centre Centre of African Studies and the Department of the History and Philosophy of Science## Other talksAdaptive Stochastic Galerkin Finite Element Approximation for Elliptic PDEs with Random Coefficients Planck Stars: theory and observations Renationalisation of the Railways. A CU Railway Club Public Debate. Skyrmions, Quantum Graphs and Carbon-12 Speak white, speak black, speak American |