On minimum matrix representation of closure operations
Discrete Applied Mathematics
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ICDT '92 Proceedings of the 4th International Conference on Database Theory
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FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
Minimum matrix representation of closure operations
Discrete Applied Mathematics
Extremal Theorems for Databases
FoIKS '02 Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems
Recent combinatorial results in the theory of relational databases
Mathematical and Computer Modelling: An International Journal
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Consider a matrix satisfying the following two properties. There are no two rows of the matrix having the same entries in two cyclically neighbouring columns. On the other hand for each subset of the columns not containing a cyclically neighbouring pair there are two rows having the same entries in these columns. In this paper the magnitude of the minimal number of the rows of such a matrix will be determined for given number of columns. Using the same method, the analogue question can be answered for some other Spernersystems, too. The heart of the proof is a combinatorial lemma, which might be interesting in itself.