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Displaying 41 – 60 of 79

On geodesics of phyllotaxis

Roland Bacher (2014)

Confluentes Mathematici

Seeds of sunflowers are often modelled by $n ⟼ ϕ_{θ} (n) = \sqrt{n} e^{2 i π n θ}$ leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance $2 π θ$ for $θ$ the golden ratio. We associate to such a map $ϕ_{θ}$ a geodesic path $γ_{θ} : ℝ_{> 0} ⟶ {PSL}_{2} (ℤ) ∖ ℍ$ of the modular curve and use it for local descriptions of the image $ϕ_{θ} (ℕ)$ of the phyllotactic map $ϕ_{θ}$ .

On Linear Sections of Lattice Packings.

H. Groemer (1986)

Monatshefte für Mathematik

On lower bounds of the density of Delone sets and holes in sequences of sphere packings.

Muraz, G., Verger-Gaugry, J.-L. (2005)

Experimental Mathematics

On Norm Three Vectors in Integral Euclidean Lattices. I.

Arnold Neumaier (1983)

Mathematische Zeitschrift

On the construction of dense lattices with a given automorphisms group

Philippe Gaborit, Gilles Zémor (2007)

Annales de l’institut Fourier

We consider the problem of constructing dense lattices in $ℝ^{n}$ with a given non trivial automorphisms group. We exhibit a family of such lattices of density at least $c n 2^{- n}$ , which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions $n$ , we exhibit a finite set of lattices that come with an automorphisms group of size $n$ , and a constant proportion of which achieves the aforementioned lower bound on the largest packing density. The algorithmic...

On the Covering Multiplicity of Lattices.

(1992)

Discrete & computational geometry

On the Euclidean minimum of some real number fields

Eva Bayer-Fluckiger, Gabriele Nebe (2005)

Journal de Théorie des Nombres de Bordeaux

General methods from [3] are applied to give good upper bounds on the Euclidean minimum of real quadratic fields and totally real cyclotomic fields of prime power discriminant.

On the lattice packing--covering ratio of finite-dimensional normed spaces

W. Banaszczyk (1990)

Colloquium Mathematicae

On the limit distribution of Frobenius numbers

Andreas Strömbergsson (2012)

Acta Arithmetica

On the Maximum of the Minimum of a Sum.

Ray Redheffer (1987)

Monatshefte für Mathematik

On the packing densities of superballs and other bodies.

A.M. Odlyzko, J.A. Rush, N.D. Elies (1991)

Inventiones mathematicae

On the section of a lattice–covering of balls

Bezdek, A. (1984)

Proceedings of the 11th Winter School on Abstract Analysis

Periodic sphere packings and the Wulff-shape.

Schnell, Uwe (1999)

Beiträge zur Algebra und Geometrie

Sausages are Good Packings.

J.M. Wills, U. Betke, M. Henk (1995)

Discrete & computational geometry

Stability of Arakelov bundles and tensor products without global sections.

Hoffmann, Norbert (2003)

Documenta Mathematica

The densest lattice in twenty-four dimensions.

Cohn, Henry, Kumar, Abhinav (2004)

Electronic Research Announcements of the American Mathematical Society [electronic only]

The sphere packing problem.

Sloane, N.J.A. (1998)

Documenta Mathematica

The star number of coverings of space with convex bodies

P. Erdös, C. Rogers (1964)

Acta Arithmetica

The strongly perfect lattices of dimension $10$

Gabriele Nebe, Boris Venkov (2000)

Journal de théorie des nombres de Bordeaux

This paper classifies the strongly perfect lattices in dimension $10$ . There are up to similarity two such lattices, $K_{10}^{'}$ and its dual lattice.

Tori in dichten gitterförmigen Kugelpackungen

O. KRÖTENHEERDT (1987)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

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