Mathematical snapshots from the computational geometry landscape.
Matrices and graphs in Euclidean geometry.
Matroid polytopes, nested sets and Bergman fans.
Matroids over a ring
We introduce the notion of a matroid over a commutative ring , assigning to every subset of the ground set an -module according to some axioms. When is a field, we recover matroids. When , and when is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, i.e. tropical linear spaces, respectively. More generally, whenever is a Dedekind domain, we extend all the usual properties and operations holding for matroids (e.g., duality), and...
Maximal elements and equilibria of generalized games for -majorized and condensing correspondences.
Maximal facet-to-facet snakes of unit cubes.
Maximization of distances of regular polygons on a circle
This paper presents the solution of a basic problem defined by J. Černý which solves a concrete everyday problem in railway and road transport (the problem of optimization of time-tables by some criteria).
Maximizing the Bregman divergence from a Bregman family
The problem to maximize the information divergence from an exponential family is generalized to the setting of Bregman divergences and suitably defined Bregman families.
Maximum convex hulls of connected systems of segments and of polyominoes.
Maximum Density Space Packing with Parallel Strings of Spheres.
Mazur's Intersection Property for Finite Dimensional Sets.
Mean Projections and Finite Packings of Convex Bodies.
Measure and Helly's Intersection Theorem for Convex Sets
Let be a uniformly bounded collection of compact convex sets in ℝ ⁿ. Katchalski extended Helly’s theorem by proving for finite ℱ that dim (⋂ ℱ) ≥ d, 0 ≤ d ≤ n, if and only if the intersection of any f(n,d) elements has dimension at least d where f(n,0) = n+1 = f(n,n) and f(n,d) = maxn+1,2n-2d+2 for 1 ≤ d ≤ n-1. An equivalent statement of Katchalski’s result for finite ℱ is that there exists δ > 0 such that the intersection of any f(n,d) elements of ℱ contains a d-dimensional ball of measure...
Measure Extensions by Conditional Atoms.
Mehrfache gitterförmige Kreis- und Kugelanordnungen.
Mehrfach-orthogonale Simplexe in Räumen konstanter Krümmung
Mesures de courbure des variétés lisses et des polyèdres
Mesures sur le cercle et convexes du plan
Methods of Perfect Coloring
Metric ellipses in Minkowski planes.
An ellipse in R2 can be defined as the locus of points for which the sum of the Euclidean distances from the two foci is constant. In this paper we will look at the sets that are obtained by considering in the above definition distances induced by arbitrary norms.