Variations on Tilings in the Manhattan Metric

被引：0
作者：
Sylvain Gravier
Michel Mollard
Charles Payan
机构：
[1] Laboratoire Leibniz,CNRS
来源：
Geometriae Dedicata | 1999年 / 76卷
关键词：
tiling; Manhattan metric.;
D O I：
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学科分类号：
摘要：
We investigate tilings of the integer lattice in the Euclidean n-dimensional space. The tiles considered here are the union of spheres defined by the Manhattan metric. We give a necessary condition for the existence of such a tiling for Zn when n ≥ 2. We prove that this condition is sufficient when n=2. Finally, we give some tilings of Zn when n ≥ 3.
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页码：265 / 274
页数：9
相关论文
共 14 条
[1]  
Adler A.(1981)Some results on one-dimensional tilings Geom. Dedicata 10 49-58
[2]  
Holryod F. C.(1982)A note on perfect Lee-codes over small alphabets Discrete Appl. Math. 4 227-228
[3]  
Astola J.(1966)The undecidability of the domino problem Mem. Amer. Math. Soc. 66 72-242
[4]  
Berger R.(1950)On bases for the set of integers Publ. Math. Debrecen 1 232-317
[5]  
De Bruijn N. G.(1970)Perfect codes in the Lee metric and the packing of polyominoes SIAM J. Appl. Math. 18 302-572
[6]  
Golomb S. W.(1998)On the nonexistence of 3-dimensional tiling in the Lee-metric Europ. J. Combin. 19 567-63
[7]  
Welch L. R.(1984)Bounds for perfect Lee-codes over small alphabet Ann. Univ. Turku., Ser. A 186 59-112
[8]  
Gravier S.(1967)Addition theorems for sets of integers Pacific J. Math. 23 107-380
[9]  
Mollard M.(1975)Nonexistence theorems on perfect Lee codes over large alphabets Inform. and Control 29 369-203
[10]  
Payan C.(1981)On mosaics consisting of multidimensional crosses Acta Math. Acad. Sci. Hungar. 38 191-undefined
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