Many Triangulated Spheres.
Mathematical morphology and poset 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 facet-to-facet snakes of unit cubes.
Mehrfach-orthogonale Simplexe in Räumen konstanter Krümmung
Minimal fixing systems for convex bodies.
Minimal-Energy Clusters of Hard Spheres.
Minimality of toric arrangements
We prove that the complement of a toric arrangement has the homotopy type of a minimal CW-complex. As a corollary we deduce that the integer cohomology of these spaces is torsionfree. We apply discrete Morse theory to the toric Salvetti complex, providing a sequence of cellular collapses that leads to a minimal complex.
Minimum Ideal Triangulations of Hyperbolic 3-Manifolds.
Minkowski valuations intertwining the special linear group
All continuous Minkowski valuations which are compatible with the special linear group are completely classified. One consequence of these classifications is a new characterization of the projection body operator.
Mirror symmetry and toric geometry.
Mittelpunktspolyeder im E4.
Mixture decompositions of exponential families using a decomposition of their sample spaces
We study the problem of finding the smallest such that every element of an exponential family can be written as a mixture of elements of another exponential family. We propose an approach based on coverings and packings of the face lattice of the corresponding convex support polytopes and results from coding theory. We show that is the smallest number for which any distribution of
Modularity in Science and Art
Modules of splines on polyhedral complexes.
Monotone Valuations on the Space of Convex Functions
We consider the space Cn of convex functions u defined in Rn with values in R ∪ {∞}, which are lower semi-continuous and such that lim|x| } ∞ u(x) = ∞. We study the valuations defined on Cn which are invariant under the composition with rigid motions, monotone and verify a certain type of continuity. We prove integral representations formulas for such valuations which are, in addition, simple or homogeneous.
More classes of stuck unknotted hexagons.
Morse index of a cyclic polygon
It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.