KELLER CUBE-TILING CONJECTURE IS FALSE IN HIGH DIMENSIONS

被引：75

作者：

LAGARIAS, JC

SHOR, PW

机构：

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 1992年 / 27卷 / 02期

关键词：

D O I：

10.1090/S0273-0979-1992-00318-X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

O. H. Keller conjectured in 1930 that in any tiling of R(n) by unit n-cubes there exist two of them having a complete facet in common. O. Perron proved this conjecture for n less-than-or-equal-to 6. We show that for all n greater-than-or-equal-to 10 there exists a tiling of R(n) by unit n-cubes such that no two n-cubes have a complete facet in common.

引用

页码：279 / 283

页数：5

共 9 条

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[2] On single and multiple covering of n-dimensional space with a cube lattice. [J].