On 2D packings of cubes in the torus

Authors:
Andrew V. Reztsov and Ian H. Sloan

Journal:
Proc. Amer. Math. Soc. **125** (1997), 17-26

MSC (1991):
Primary 05B40; Secondary 11H31, 52C15, 65D32

MathSciNet review:
1401751

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Abstract: The 2D packings of cubes (i.e. squares) in the torus are considered. We obtain the exact expression for the quantity , the maximal number of 2D cubes in a packing. (Here is the length of sides of cubes, .) Corresponding best packings are constructed. Both rank 1 best lattice packings and rank 2 best lattice packings are given.

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Additional Information

**Andrew V. Reztsov**

Affiliation:
Research Fellow, Division of Science and Technology, Tamaki Campus, The University of Auckland, Private Bag 92019, Auckland, New Zealand

Email:
a.reztsov@auckland.ac.nz

**Ian H. Sloan**

Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, New South Wales, Australia

Email:
I.Sloan@unsw.edu.au

DOI:
https://doi.org/10.1090/S0002-9939-97-03930-0

Received by editor(s):
June 16, 1995

Communicated by:
William W. Adams

Article copyright:
© Copyright 1997
American Mathematical Society