The Venkov-McMullen Theorem and Stein’s Phenomenon

  • Chuanming Zong
  • James J. Dudziak
Part of the Universitext book series (UTX)

Abstract

Let M be an n-dimensional compact set with interior points. If there exists a set of points X such that
$$\bigcup\limits_{x \in X} {\left( {M + x} \right)} = {R^n}$$
and
$$\left( {\operatorname{int} \left( M \right) + {x_1}} \right) \cap \left( {\operatorname{int} \left( M \right) + {x_2}} \right) = 0$$
whenever x1, x2X with x1x2, then we call M a translative tile. In addition, if X is a lattice in R n , then we call M a lattice tile.

Keywords

Stein Dition Delone 

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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Chuanming Zong
    • 1
  • James J. Dudziak
    • 2
  1. 1.Institute of MathematicsThe Chinese Academy of SciencesBeijingPR China
  2. 2.Department of MathematicsBucknell UniversityLewisburgUSA

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