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)


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.


Line Parallel Discrete Mathematic Common Boundary Extremal Graph Horizontal Side 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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. 

Personalised recommendations