Penny-Packing and Two-Dimensional Codes.
Perfect Delaunay polytopes in low dimensions.
Perfekte Rechteckzerlegung.
Periodic factorization of a finite Abelian 2-group.
Periodic sphere packings and the Wulff-shape.
Permanence of moment estimates for p-products of convex bodies
It is shown that two inequalities concerning second and fourth moments of isotropic normalized convex bodies in ℝⁿ are permanent under forming p-products. These inequalities are connected with a concentration of mass property as well as with a central limit property. An essential tool are certain monotonicity properties of the Γ-function.
Perturbations and approximations of support functions of convex bodies.
Perturbing the hexagonal circle packing: a percolation perspective
We consider the hexagonal circle packing with radius and perturb it by letting the circles move as independent Brownian motions for time . It is shown that, for large enough , if is the point process given by the center of the circles at time , then, as , the critical radius for circles centered at to contain an infinite component converges to that of continuum percolation (which was shown – based on a Monte Carlo estimate – by Balister, Bollobás and Walters to be strictly bigger than...
Petrie-Coxeter maps revisited.
Pflasterungen des Raumes mit Pyramiden und Doppelpyramiden.
Pflasterungen von Rechtecken mit Steinen vom Typ 1 x j.
Piecewise affine selections for piecewise polyhedral multifunctions and metric projections.
Piecewise Convex Curves and their Integral Representation
2000 Mathematics Subject Classification: 52A10.A convex arc in the plane is introduced as an oriented arc G satisfying the following condition: For any three of its points c1 < c2 < c3 the triangle c1c2c3 is counter-clockwise oriented. It is proved that each such arc G is a closed and connected subset of the boundary of the set FG being the convex hull of G. It is shown that the convex arcs are rectifyable and admit a representation in the natural parameter by the Riemann-Stieltjes integral...
Piecewise polynomial functions, convex polytopes and enumerative geometry
Placing and moving spheres in the gaps of a cylinder packing.
Planar anisotropy revisited
The paper concerns estimation of anisotropy of planar fibre systems using the relation between the rose of directions and the rose of intersections. The discussion about the properties of the Steiner compact estimator is based on both theoretical and simulation results. The approach based on the distribution of the Prokhorov distance between the estimated and true rose of directions is developed. Finally the curved test systems are investigated in both Fourier and Steiner compact analysis of anisotropy....
Planar graphs as minimal resolutions of trivariate monomial ideals.
Planning a Purely Translational Motion for a Convex Object in Two-Dimensional Space Using Generalized Voronoi Diagrams.
Platonic hypermaps.
Poincaré Inequalities and Moment Maps
We discuss a method for obtaining Poincaré-type inequalities on arbitrary convex bodies in . Our technique involves a dual version of Bochner’s formula and a certain moment map, and it also applies to some non-convex sets. In particular, we generalize the central limit theorem for convex bodies to a class of non-convex domains, including the unit balls of -spaces in for .