On-Line Covering a Cube by a Sequence of Cubes.
On-Line Covering the Unit Cube by Cubes.
On-line Covering the Unit Square with Squares
The unit square can be on-line covered with any sequence of squares whose total area is not smaller than 4.
On-line packing regular boxes in the unit cube
We describe a class of boxes such that every sequence of boxes from this class of total volume smaller than or equal to 1 can be on-line packed in the unit cube.
On-line packing sequences of segments, cubes and boxes.
On-line Packing Squares into n Unit Squares
If n ≥ 3, then any sequence of squares of side lengths not greater than 1 whose total area does not exceed ¼(n+1) can be on-line packed into n unit squares.
On-line -adic covering by the method of the -th segment and its application to on-line covering by cubes.
Optimal bounds for the colored Tverberg problem
We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.
Optimal packings for filled rings of circles
General circle packings are arrangements of circles on a given surface such that no two circles overlap except at tangent points. In this paper, we examine the optimal arrangement of circles centered on concentric annuli, in what we term rings. Our motivation for this is two-fold: first, certain industrial applications of circle packing naturally allow for filled rings of circles; second, any packing of circles within a circle admits a ring structure if one allows for irregular spacing of circles...
Optimal Spherical Packing of Circles and Hilbert's 14th Problem
Optimal substructures in optimal and approximate circle packings.
Optimisation hybride par colonies de fourmis pour le problème de découpe à deux dimensions
Nous nous intéressons dans cet article au problème de découpe guillotine en deux dimensions noté 2BP/O/G. Il s'agit de découper un certain nombre de pièces rectangulaires dans un ensemble de plaques de matière première, elles même rectangulaires et identiques. Celles-ci sont disponibles en quantité illimitée. L'objectif est de minimiser le nombre de plaques utilisées pour satisfaire la demande, en appliquant une succession de coupes, dites guillotines, allant de bout en bout. Nous proposons une approche...
Oriented Matroids with Few Mutations.
Outer boundaries of self-similar tiles.
Packing 10 or 11 unit squares in a square.
Packing and covering a unit equilateral triangle with equilateral triangles.
Packing lines, planes, etc.: Packings in Grassmannian spaces.
Packing of 180 equal circles on a sphere.
Packing unit squares in a rectangle.
Packing unit squares in squares: A survey and new results.