Nonexistence of face-to-face four-dimensional tilings in the Lee metric
نویسنده
چکیده
A family of n-dimensional Lee spheres L is a tiling of Rn , if ∪L = Rn and for every Lu , Lv ∈ L, the intersection Lu ∩ Lv is contained in the boundary of Lu . If neighboring Lee spheres meet along entire (n−1)-dimensional faces, then L is called a face-to-face tiling. We prove the nonexistence of a face-to-face tiling of R4 with Lee spheres of different radii. c © 2005 Elsevier Ltd. All rights reserved. MSC: 52C22; 94B60; 68R05
منابع مشابه
Tilings in Lee metric
Gravier et al. proved [S. Gravier, M. Mollard, Ch. Payan, On the existence of three-dimensional tiling in the Lee metric, European J. Combin. 19 (1998) 567–572] that there is no tiling of the three-dimensional space R3 with Lee spheres of radius at least 2. In particular, this verifies the Golomb–Welch conjecture for n = 3. Špacapan, [S. Špacapan, Non-existence of face-to-face four-dimensional ...
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ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 28 شماره
صفحات -
تاریخ انتشار 2007