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On Partitions of a Rectangle into Rectangles with Restricted Number of Cross Sections

  • R. Ahlswede
  • A. A. Yudin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)

Abstract

Consider partitions of a rectangle into rectangles with restricted number of cross sections. The problem has an information theoretic flavor (in the spirit of [3]): richness of two dimensional pictures under 1–dimensional restrictions of from local information to global information.

We present two approaches to upper bound the cardinality of such partitions: a combinatorial recursion and harmonic analysis.

Keywords

Line Parallel Discrete Mathematic Common Boundary Extremal Graph Horizontal Side 
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References

  1. 1.
    Bollobás, B.: Extremal Graph Theory. Academic Press, London (1978)MATHGoogle Scholar
  2. 2.
    Bourgain, J.: Harmonic analysis and combinatorics: how much may they contribute to each other? In: Arnold, V., Atiyah, M., Lax, P., Mazur, B. (eds.), pp. 13–32. Mathematics: Frontiers and Perspectives (2000)Google Scholar
  3. 3.
    Ahlswede, R.: Coloring hypergraphs: A new approach to multi–user source coding, Part I. Journ. of Combinatorics, Information and System Sciences 4(1), 76–115 (1979); Part II 5(3), 220–268 (1980)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • R. Ahlswede
    • 1
  • A. A. Yudin
    • 2
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2. 

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