On partitions of discrete boxes

  • Authors:

  • Noga Alon;Tom Boham;Ron Holzman;Daniel J. Kleitman

  • Affiliations:

  • Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel;Department of Mathematics, Carnegie Mellon University, Pittsburgh;Department of Mathematics, Massachusetts Institute of Technology, Cambridge;Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel

  • Venue:
  • Discrete Mathematics - Kleitman and combinatorics: a celebration
  • Year:
  • 2002

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Abstract

We prove that any partition of an n-dimensional discrete box into nontrivial sub-boxes must consist of at least 2n sub-boxes, and consider some extensions of this theorem.