Nonexistence of face-to-face four-dimensional tilings in the Lee metric

Authors:
Simon Špacapan
Affiliations:
University of Maribor, FME, Smetanova, Maribor, Slovenia
Venue:
European Journal of Combinatorics
Year:
2007

Citing 3
Cited 3

Algorithms (2nd ed.)

Algorithms (2nd ed.)
On the non-existence of 3-dimensional tiling in the Lee metric

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Nonexistence of face-to-face four-dimensional tilings in the Lee metric

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Nonexistence of face-to-face four-dimensional tilings in the Lee metric

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Tilings in Lee metric

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A new approach towards the Golomb-Welch conjecture

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Abstract

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.