Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Rational tilings by $ n$-dimensional crosses. II

Author: S. Szabó
Journal: Proc. Amer. Math. Soc. 93 (1985), 569-577
MSC: Primary 05B45; Secondary 11H31, 20K01, 52A45
MathSciNet review: 776181
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The union of translates of a closed unit $ n$-dimensional cube whose edges are parallel to the coordinate unit vectors $ {{\mathbf{e}}_1}, \ldots ,{{\mathbf{e}}_n}$ and whose centers are $ i{{\mathbf{e}}_j},\left\vert i \right\vert \leq k,1 \leq j \leq n$, is called a $ (k,n)$-cross. A system of translates of a $ (k,n)$-cross is called an integer (a rational) lattice tiling if its union is $ n$-space and the interiors of its elements are disjoint, the translates form a lattice and each translation vector of the lattice has integer (rational) coordinates. In this paper we shall continue the examination of rational cross tilings begun in [2], constructing rational lattice tilings by crosses that have noninteger coordinates on several axes.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05B45, 11H31, 20K01, 52A45

Retrieve articles in all journals with MSC: 05B45, 11H31, 20K01, 52A45

Additional Information

PII: S 0002-9939(1985)0776181-9
Keywords: Factorization splitting and partition of abelian groups, crosses, semicrosses, lattice tiling
Article copyright: © Copyright 1985 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia