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Nonexistence of face-to face four-dimensional tilings in the Lee metric
Simon Špacapan, 2007, original scientific article

Abstract: A family of ▫$n$▫-dimensional Lee spheres ▫$mathcal{L}$▫ is a tiling of ▫${mathbb{R}}^n$▫ if ▫$cupmathcal{L} = {mathbb{R}}^n$▫ and for every ▫$L_u, L_v in mathcal{L}$▫, the intersection ▫$L_u cap L_v$▫ is contained in the boundary of ▫$L_u$▫. If neighboring Lee spheres meet along entire ▫$(n-1)$▫-dimensional faces, then ▫$mathcal{L}$▫ is called a face-to-face tiling. We prove nonexistence of a face-to-face tiling of ▫${mathbb{R}}^4$▫, with Lee spheres of different radii.
Keywords: delitev, Leejeva metrika, popolne kode, tiling, Lee metric, perfect codes
Published: 10.07.2015; Views: 338; Downloads: 43
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