A combinatorial approach for Keller's conjecture

K. Corrádi; S. Szabó

doi:10.1007/bf01946848

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Periodica Mathematica Hungarica

Volume/Issue:: Volume 21: Issue 2

A combinatorial approach for Keller's conjecture

Authors:

K. Corrádi

K. Corrádi

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S. Szabó

S. Szabó

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Pages:: 95–100

Online Publication Date:: 01 Aug 2005

Publication Date:: 01 Jun 1990

Article Category:: Research Article

DOI:: https://doi.org/10.1007/bf01946848

Keywords:: Primary 10E30; Secondary 20K01; factorization of finite abelian groups

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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 graphsΓ_n has a 2ⁿ size clique. The 4ⁿ vertices ofΓ_n 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 ofΓ_n forn≤5.

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Periodica Mathematica Hungarica

Print ISSN:: 0031-5303

Online ISSN:: 1588-2829

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Periodica Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1971
Volumes per Year	2
Issues per Year	4
Founder	Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's Address	H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0031-5303 (Print)
ISSN	1588-2829 (Online)