The number of maximal independent sets in a tree
SIAM Journal on Algebraic and Discrete Methods
The number of maximal independent sets in a connected graph
Discrete Mathematics
A note on independent sets in trees
SIAM Journal on Discrete Mathematics
On minimum matrix representation of closure operations
Discrete Applied Mathematics
Perfect error-correcting databases
Discrete Applied Mathematics
Two conjectures of Demetrovics, Furedi, and Katona, concerning partitions
Discrete Mathematics
The design of relational databases
The design of relational databases
The number of maximal independent sets in triangle-free graphs
SIAM Journal on Discrete Mathematics
Maximal independent sets in bipartite graphs
Journal of Graph Theory
Minimum matrix representation of Sperner systems
Discrete Applied Mathematics
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Combinatorial and Algebraic Results for Database Relations
ICDT '92 Proceedings of the 4th International Conference on Database Theory
Extremal Combinatorial Problems in Relational Data Base
FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
Some contributions to the minimum representation problem of key systems
FoIKS'06 Proceedings of the 4th international conference on Foundations of Information and Knowledge Systems
On the existence of armstrong data trees for XML functional dependencies
FoIKS'10 Proceedings of the 6th international conference on Foundations of Information and Knowledge Systems
| Hi-index | 0.00 |
We say, that a subset K of the columns of a matrix is called a key, if every two rows that agree in the columns of K agree also in all columns of the matrix. A matrix represents a Sperner system K, if the system of minimal keys is exactly K. It is known, that such a representation always exists. In this paper we show, that the maximum of the minimum number of rows, that are needed to represent a Sperner system of only two element sets is 3(n/3+o(n)). We consider this problem for other classes of Sperner systems (e.g., for the class of trees, i.e. each minimal key has cardinality two, and the keys form a tree), too. The concept of keys plays an important role in database theory.