Rational tilings by -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
Abstract: The union of translates of a closed unit -dimensional cube whose edges are parallel to the coordinate unit vectors and whose centers are , is called a -cross. A system of translates of a -cross is called an integer (a rational) lattice tiling if its union is -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 , constructing rational lattice tilings by crosses that have noninteger coordinates on several axes.
Keywords: Factorization splitting and partition of abelian groups, crosses, semicrosses, lattice tiling
Article copyright: © Copyright 1985 American Mathematical Society