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

Abstract

A family of ▫$n$▫-dimensional Lee spheres ▫$\mathcal{L}$▫ is a tiling of ▫${\mathbb{R}}^n$▫ if ▫$\cup\mathcal{L} = {\mathbb{R}}^n$▫ 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;

Data

Language:	English
Year of publishing:	2007
Typology:	1.01 - Original Scientific Article
Organization:	UM FS - Faculty of Mechanical Engineering
UDC:	514.174
COBISS:	14128985
ISSN:	0195-6698
Views:	658
Downloads:	72
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Unknown
Secondary title:	Neobstoj regularne štiridimenzionalne delitve v Leejevi metriki
Secondary keywords:	delitev;Leejeva metrika;popolne kode;
Type (COBISS):	Not categorized
Pages:	str. 127-133
Volume:	ǂVol. ǂ28
Issue:	ǂno. ǂ1
Chronology:	2007
ID:	1472869