On Well-Rounded Sublattices of the Hexagonal Lattice

Authors

Lenny Fukshansky, Claremont McKenna CollegeFollow
Daniel Moore, Loyola Marymount University
R. Andrew Ohana, University of Washington
Whitney Zeldow, San Francisco State University

Document Type

Article

Department

Mathematics (CMC)

Publication Date

12-6-2010

Abstract

We produce an explicit parameterization of well-rounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest signal-to-noise ratio of well-rounded sublattices of the hexagonal lattice of a fixed index. This investigation parallels earlier work by Bernstein, Sloane, and Wright where similar questions were addressed on the space of all sublattices of the hexagonal lattice. Our restriction is motivated by the importance of well-rounded lattices for discrete optimization problems. Finally, we also discuss the existence of a natural combinatorial structure on the set of similarity classes of well-rounded sublattices of the hexagonal lattice, induced by the action of a certain matrix monoid.

Comments

This article (in PDF form) can also be found at http://arxiv.org/pdf/1007.2667v2.pdf

Rights Information

© 2010 Elsevier B.V.

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Terms of Use for work posted in Scholarship@Claremont.

DOI

http://dx.doi.org/10.1016/j.disc.2010.07.014

Recommended Citation

Fukshansky, Lenny, Daniel Moore, R. Andrew Ohana, and Whitney Zeldow. "On Well-Rounded Sublattices of the Hexagonal Lattice." Discrete Mathematics 310.23 (2010): 3287-3302. Web.