Minimum matrix representation of some key system Original Research Article

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 Sperner-systems, too. The heart of the proof is a combinatorial lemma, which might be interesting in itself.