- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Minimum saturated families
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Minimum saturated families Letzter, Shoham
Description
A family $F$ of subsets of $[n]$ is called $s$-saturated if it contains no $s$ pairwise disjoint sets, and moreover, no set can be added to $F$ while preserving this property. Over 40 years ago, Erdos and Kleitman conjectured that an $s$-saturated family of subsets of $[n]$ has size at least $(1 - 2/(s-1))2n$. We show that every $s$-saturated family has size at least $(1 - 1/s)2n$, thus providing the first non-trivial progress on the conjecture.
Item Metadata
| Title |
Minimum saturated families
|
| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
| Date Issued |
2019-09-03T09:45
|
| Description |
A family $F$ of subsets of $[n]$ is called $s$-saturated if it contains no $s$ pairwise disjoint sets, and moreover, no set can be added to $F$ while preserving this property. Over 40 years ago, Erdos and Kleitman conjectured that an $s$-saturated family of subsets of $[n]$ has size at least $(1 - 2/(s-1))2n$. We show that every $s$-saturated family has size at least $(1 - 1/s)2n$, thus providing the first non-trivial progress on the conjecture.
|
| Extent |
29.0 minutes
|
| Subject | |
| Type | |
| File Format |
video/mp4
|
| Language |
eng
|
| Notes |
Author affiliation: ETH Zurich
|
| Series | |
| Date Available |
2020-03-02
|
| Provider |
Vancouver : University of British Columbia Library
|
| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0388812
|
| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
|
| Scholarly Level |
Postdoctoral
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International