Moments of inertia associated with the lozenge tilings of a hexagon.
Monomer-dimer tatami tilings of rectangular regions.
...-Morphic Sets of Prototiles.
Motion of spirals by crystalline curvature
Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.
Movable configurations.
Multigrid-convergence of digital curvature estimators
Many methods have been proposed to estimate differential geometric quantities like curvature(s) on discrete data. A common characteristics is that they require (at least) one user-given scale or window parameter, which smoothes data to take care of both the sampling rate and possible perturbations. Digital shapes are specific discrete approximation of Euclidean shapes, which come from their digitization at a given grid step. They are thus subsets of the digital plane . A digital geometric estimator...
Multiple Lattice Packings and Coverings of Spheres.
Multiple tilings by cubes with no shared faces.
Multiple Tilings of n-Dimensional Space by Unit Cubes.
New bounds in some transference theorems in the geometry of numbers.
New conjectural lower bounds on the optimal density of sphere packings.
New lower bounds for Heilbronn numbers.
New Upper Bounds for Some Spherical Codes
The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases...
New upper bounds on sphere packings. II.
Non-integer lattice tilings by (k, n) truncated crosses.
Nontiles and nonfacets for the Euclidean space, spherical complexes and convex polytopes.
Normal polytopes, triangulations, and Koszul algebras.
Note on Lattice-Point-Free Convex Bodies.
Note on Packing of 19 Equal Circles on a Sphere.
Note to a paper of Bambah, Rogers and Zassenhaus