Periodica Mathematica Hungarica

, Volume 21, Issue 2, pp 95–100 | Cite as

A combinatorial approach for Keller's conjecture

  • K. Corrádi
  • S. Szabó
Article

Abstract

The statement, that in a tiling by translates of ann-dimensional cube there are two cubes having common (n-1)-dimensional faces, is known as Keller's conjecture. We shall prove that there is a counterexample for this conjecture if and only if the following graphsΓn has a 2n size clique. The 4n vertices ofΓn aren-tuples of integers 0, 1, 2, and 3. A pair of thesen-tuples are adjacent if there is a position at which the difference of the corresponding components is 2 modulo 4 and if there is a further position at which the corresponding components are different. We will give the size of the maximal cliques ofΓn forn≤5.

Mathematics Subject Classification 1980/85

Primary 10E30 Secondary 20K01 

Key words and phrases

Cube tilings Keller's conjecture factorization of finite abelian groups 

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References

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Copyright information

© Akadémiai Kiadó 1990

Authors and Affiliations

  • K. Corrádi
    • 1
    • 2
  • S. Szabó
    • 1
    • 2
  1. 1.Dept. of computer TechnEötvös Loránd univBudapestHungary
  2. 2.Dept. of civil engineering mathTech. univ. BudapestBudapestHungary

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