The Mayer-Vietoris and IC Equations for Convex Polytopes.
The mean of a maximum likelihood estimator associated with the Brownian bridge.
The mean surface area of the boxes circumscribed about a convex body
The minimal perimeter for confined deformable bubbles of equal area.
The minimum mean width translation cover for sets of diameter one.
The Minlos lemma for positive-definite functions on additive subgroups of
Let H be a real Hilbert space. It is well known that a positive-definite function φ on H is the Fourier transform of a Radon measure on the dual space if (and only if) φ is continuous in the Sazonov topology (resp. the Gross topology) on H. Let G be an additive subgroup of H and let (resp. ) be the character group endowed with the topology of uniform convergence on precompact (resp. bounded) subsets of G. It is proved that if a positive-definite function φ on G is continuous in the Gross topology,...
The moduli space of n tropically collinear points in Rd.
The tropical semiring (R, min, +) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of labeled n-point configurations lying on a tropical line in d-space, which is interpretable as the space of n-species phylogenetic trees. This is equivalent to the space of n x d matrices of tropical rank two, a simplicial complex. We prove that this simplicial complex is shellable for dimension...
The multiplicity of partial coverings of space
The Newton polygon of a product of power series.
The Number of Different Distances Determined by a Set of Points in the Euclidean Plane.
The number of vertices of a Fano polytope
Let be a Gorenstein, -factorial, toric Fano variety. We prove two conjectures on the maximal Picard number of in terms of its dimension and its pseudo-index, and characterize the boundary cases. Equivalently, we determine the maximal number of vertices of a simplicial reflexive polytope.
The operation of infimal convolution [Book]
The optimal ball and horoball packings of the Coxeter tilings in the hyperbolic 3-space.
The optimal ball and horoball packings to the Coxeter honeycombs in the hyperbolic -space.
The Orthogonal Convex Skull Problem.
The partition problem for equifacetal simplices.
The pentagram map.
The pentagram map is recurrent.
The plank problem for symmetric bodies.
The Polytope of m-Subspaces of a Finite Affine Space
The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces of a finite affine space. The particular case of the hyperplane polytope has been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general m-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the...