Abstract
A matrixM withn columns represents a closure operationF(A), (A⊂X, |X|=n) if for anyA, any two rows equal in the columns corresponding toA are also equal inF(A). Letm(F) be the minimum number of rows of the matrices representingF. Lower and upper estimates on maxm(F) are given where max runs over the set of all closure operations onn elements.
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References
W. W. Armstrong, Dependency Structures of Data Base Relationships, in:Information Processing 74, North-Holland, Amsterdam, 1974, pp. 580–583.
J. Demetrovics andGy. Gyepesi, On the functional dependency and some generalizations of it,Acta Cybernetica 5 (1981) 295–305.
D. J. Kleitman, Extremal Properties of Collections of Subsets Containing No Two Sets and Their Union,J. Combinatorial Theory (A) 20 (1976) 390–392.
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Demetrovics, J., Gyepesi, G. A note on minimal matrix representation of closure operations. Combinatorica 3, 177–179 (1983). https://doi.org/10.1007/BF02579291
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DOI: https://doi.org/10.1007/BF02579291