On counting Sperner families
β Scribed by Raymond Balbes
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 405 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The profile of a family of subsets of an n-element set is a vector f = (f,, , f,), where fk denotes the number of k-element sets in the family. Using a new method the extreme points of the convex hull of the profiles of all complementfree Sperner families over an n-element set are determined.
We explore a problem of Frankl (1989). A family ~ of subsets of {1, 2, ..., m} is said to have trace Kk if there is a subset SC\_{1,2 ..... m} with IS] = k so that {FNSIF C .~} yields all 2 k possible subsets. Frankl (1989) conjectured that a family ~ which is an antichain (in poser given by C\_ ord
Color the elements of a finite set S with two colors. A collection of subsets of S is called a 2-part Sperner family if whenever for two distinct sets A and B in this collection we have A c B then B -A has elements of S of both colors. All 2-part Sperner families of maximum size were characterized i