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Keller's cube-tiling conjecture is false in high dimensions
Author(s):
Jeffrey
C.
Lagarias;
Peter
W.
Shor
Journal:
Bull. Amer. Math. Soc.
27
(1992),
279-283.
MSC (1991):
Primary 52C22, Secondary, 05B45;
Secondary 05B45
MathSciNet review:
1155280
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References:
- [1]
- K. Corr\'adi and S. Szab\'o, A combinatorial approach for Keller{\rm '}s conjecture, Period. Math. Hungar. \textbf{21} (1990), 91--100. MR 1070948
- [2]
- G. Haj\'os, \"Uber einfache und mehrfache Bedeckung des $n$-dimensionalen Raumes mit einen W\"urfelgitter, Math. Z. \textbf{47} (1942), 427--467. MR 6425
- [3]
- G. Haj\'os, Sur la factorisation des groupes abelians, \v Casopis P\v est. Mat. Fys. \textbf{74} (1950), 157--162. MR 45727
- [4]
- O. H. Keller, \"Uber die l\"uckenlose Einf\"ullung des Raumes mit W\"urfeln, J. Reine Angew, Math. \textbf{163} (1930), 231--248. MR
- [5]
- H. Minkowski, Diophantische Approximationen, Teubner, Leipzig, 1907 \afterall (Reprint: 1961 Physica-Verlag, W\"urzberg.) [see Chapter 2, \S 4 and Chapter 3, \S 7. Minkowski's Conjecture appears on p. 28 and its geometric interpretation on p. 74.]. MR 201382
- [6]
- O. Perron, \"Uber l\"uckenlose Ausf\"ullung des $n$-dimensionalen Raumes durch kongruente W\"urfel{\rm , I, II}, Math. Z. \textbf{46} (1940), 1--26, 161--180. MR
- [7]
- S. K. Stein, Algebraic tiling, Amer. Math. Monthly \textbf{81} (1974), 445--462. MR 340063
- [8]
- S. Szab\'o, A reduction of Keller{\rm '}s conjecture, Period. Math. Hungar. \textbf{17} (1986), 265--277. MR 866636
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Additional Information:
DOI:
10.1090/S0273-0979-1992-00318-X
PII:
S 0273-0979(1992)00318-X
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