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.
Dihedral f-tilings of the sphere by equilateral and scalene triangles. III.
Dihedral f-tilings of the sphere by equilateral and scalene triangles-I
Dihedral f-tilings of the sphere by spherical triangles and equiangular well-centered quadrangles.
Discrete convexity.
Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices
Let be a flat surface of genus with cone type singularities. Given a bipartite graph isoradially embedded in , we define discrete analogs of the Dirac operators on . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair for these discrete Dirac operators to be Kasteleyn matrices of the graph . As a consequence, if these conditions are met, the partition function of the dimer...
Discrete geometry and numeration
Discrete isothermic surfaces.
Disks with Special Properties of Densest Packings.
Dissections into equilateral triangles.
Dissections of Regular Polygons into Triangles of Equal Areas.
Distributing points on the sphere. I.