On well-rounded sublattices of the hexagonal lattice
نویسندگان
چکیده
منابع مشابه
On well-rounded sublattices of the hexagonal lattice
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, ...
متن کاملClaremont Reu Abstract of L. Fukshansky’s Group: on Well-rounded Sublattices of the Hexagonal Lattice
Kepler’s Conjecture, recently proved by T. Hales, states that the densest packing of spheres in 3-space has spheres centered along the face-centered cubic (fcc) lattice. A lattice is a free Z-module formed by taking the span of a collection of linearly independent vectors in R over the integers. The two-dimensional analogue of Kepler’s Conjecture, proved by L. F. Toth in 1940, states that the d...
متن کاملOn Distribution of Well - Rounded Sublattices
A lattice is called well-rounded if its minimal vectors span the corresponding Euclidean space. In this paper we completely describe well-rounded full-rank sublattices of Z 2 , as well as their determinant and minima sets. We show that the determinant set has positive density, deriving an explicit lower bound for it, while the minima set has density 0. We also produce formulas for the number of...
متن کاملOn sublattices of the hexagonal lattice
How many sublattices of index N are there in the planar hexagonal lattice? Which of them are the best from the point of view of packing density, signal-to-noise ratio, or energy? We answer the first question completely and give partial answers to the other questions.
متن کاملOn Distribution of Well-Rounded Sublattices of Z2
A lattice is called well-rounded if its minimal vectors span the corresponding Euclidean space. In this paper we completely describe wellrounded full-rank sublattices of Z, as well as their determinant and minima sets. We show that the determinant set has positive density, deriving an explicit lower bound for it, while the minima set has density 0. We also produce formulas for the number of suc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2010.07.014