Minimum matrix representation of closure operations

  • Authors:
  • J. Demetrovics;Z. Füredi;G. O. H. Katona

  • Affiliations:
  • -;-;-

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 1985

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Abstract

Let a be a column of the m x n matrix M and A a set of its columns. We say that A implies a iff M contains no two rows equal in A but different in a. It is easy to see that if @?"M(A) denotes the columns implied by A, than @?"M(A) is a closure operation. We say that M represents this closure operation. s() is the minimum number of the rows of the matrices representing a given closure operation. s(@?) is determined for some particular closure operations.