NDLI: On Integral Well-rounded Lattices in the Plane

Content Provider	Springer Nature Link
Author	Fukshansky, Lenny Henshaw, Glenn Liao, Philip Prince, Matthew Sun, Xun Whitehead, Samuel
Copyright Year	2012
Abstract	We investigate distribution of integral well-rounded lattices in the plane, parameterizing the set of their similarity classes by solutions of the family of Pell-type Diophantine equations of the form x 2+Dy 2=z 2 where D>0 is squarefree. We apply this parameterization to the study of the greatest minimal norm and the highest signal-to-noise ratio on the set of such lattices with fixed determinant, also estimating cardinality of these sets (up to rotation and reflection) for each determinant value. This investigation extends previous work of the first author in the specific cases of integer and hexagonal lattices and is motivated by the importance of integral well-rounded lattices for discrete optimization problems. We briefly discuss an application of our results to planar lattice transmitter networks.
Starting Page	735
Ending Page	748
Page Count	14
File Format	PDF
ISSN	01795376
Journal	Discrete & Computational Geometry
Volume Number	48
Issue Number	3
e-ISSN	14320444
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-06-06
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Integral lattices Well-rounded lattices Binary and ternary quadratic forms Epstein zeta function Combinatorics Computational Mathematics and Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Discrete Mathematics and Combinatorics Theoretical Computer Science Computational Theory and Mathematics Geometry and Topology

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