Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

What is known about unit cubes


Author: Chuanming Zong
Journal: Bull. Amer. Math. Soc. 42 (2005), 181-211
MSC (2000): Primary 05A15, 05B20, 05B25, 05B45, 11H31, 11J13, 15A33, 20K01, 28A25, 52B05, 52C20, 52C22
Published electronically: January 26, 2005
MathSciNet review: 2133310
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Unit cubes, from any point of view, are among the simplest and the most important objects in $n$-dimensional Euclidean space. In fact, as one will see from this survey, they are not simple at all. On the one hand, the known results about them have been achieved by employing complicated machineries from Number Theory, Group Theory, Probability Theory, Matrix Theory, Hyperbolic Geometry, Combinatorics, etc.; on the other hand, the answers for many basic problems about them are still missing. In addition, the geometry of unit cubes does serve as a meeting point for several applied subjects such as Design Theory, Coding Theory, etc. The purpose of this article is to figure out what is known about the unit cubes and what do we want to know about them.


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


Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 05A15, 05B20, 05B25, 05B45, 11H31, 11J13, 15A33, 20K01, 28A25, 52B05, 52C20, 52C22

Retrieve articles in all journals with MSC (2000): 05A15, 05B20, 05B25, 05B45, 11H31, 11J13, 15A33, 20K01, 28A25, 52B05, 52C20, 52C22


Additional Information

Chuanming Zong
Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: cmzong@math.pku.edu.cn

DOI: http://dx.doi.org/10.1090/S0273-0979-05-01050-5
PII: S 0273-0979(05)01050-5
Received by editor(s): June 9, 2004
Published electronically: January 26, 2005
Additional Notes: This work was supported by the National Science Foundation of China, 973 Project and a special grant from Peking University.
Article copyright: © Copyright 2005 American Mathematical Society