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Dense packings of equal disks in an equilateral triangle: From 22 to 34 and beyond.
Dense packings of equal spheres in a cube.
Densest Packing of Six Equal Circles in a Square.
Densest Packing of Translates of the Union of Two Circles.
Densest Packings of Typical Convex Sets Are Not Lattice-Like .
Densité maximale des empilements de sphères en dimension 3
Determinant formulae for some tiling problems and application to fully packed loops
We present a number of determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration.
Dichteste gitterförmige Lagerung kongruenter Körper
Dichteste Packungen von gleichen Kreisen in einem Quadrat.
Die dichteste Packung von 14 Kreisen in einem Quadrat
Die dichteste Packung von 36 Kreisen in einem Quadrat
Die flächenkleinsten Vierecke, die zwei gegebene, sich von außen berührende Kreise enthalten
Die Zerlegung spezieller Einheitskreisüberdeckungen in drei Einheitskreispackungen
Die Zerlegung von gitterpunktförmigen 2-fachen Einheitskreispackungen in drei Einheitskreispackungen
Diffeomorphic types of the complements of arrangements of hyperplanes
Diffraction spectra of weighted Delone sets on beta-lattices with beta a quadratic unitary Pisot number
The Fourier transform of a weighted Dirac comb of beta-integers is characterized within the framework of the theory of Distributions, in particular its pure point part which corresponds to the Bragg part of the diffraction spectrum. The corresponding intensity function on this Bragg part is computed. We deduce the diffraction spectrum of weighted Delone sets on beta-lattices in the split case for the weight, when beta is the golden mean.
Digit sets of integral self-affine tiles with prime determinant
Let M ∈ Mₙ(ℤ) be expanding such that |det(M)| = p is a prime and pℤⁿ ⊈ M²(ℤⁿ). Let D ⊂ ℤⁿ be a finite set with |D| = |det(M)|. Suppose the attractor T(M,D) of the iterated function system has positive Lebesgue measure. We prove that (i) if D ⊈ M(ℤⁿ), then D is a complete set of coset representatives of ℤⁿ/M(ℤⁿ); (ii) if D ⊆ M(ℤⁿ), then there exists a positive integer γ such that , where D₀ is a complete set of coset representatives of ℤⁿ/M(ℤⁿ). This improves the corresponding results of Kenyon,...
Dihedral -tilings of the sphere by equilateral and scalene triangles. II.
Dihedral -tilings of the sphere by rhombi and triangles.