DCG
2010
13 years 6 months ago
2010
Abstract The purpose of this paper is to establish an inequality connecting the lattice point enumerator of a 0-symmetric convex body with its successive minima. To this end, we in...
DCG
2010
13 years 8 months ago
2010
Fix a finite set of points in Euclidean n-space En , thought of as a point-cloud sampling of a certain domain D En . The VietorisRips complex is a combinatorial simplicial complex...
DCG
2010
13 years 8 months ago
2010
Abstract. The Topological Radon Theorem states that, for every continuous function from the boundary of a (d + 1)-dimensional simplex into Rn , there exist a pair of disjoint faces...
DCG
2010
13 years 8 months ago
2010
We show that any family of sets uniformly definable in an ominimal structure has an extended compression scheme of size equal to the number of parameters in the defining formula. ...
DCG
2010
13 years 10 months ago
2010
A new approach to algorithmic computation of the homology of spaces and maps is presented. The key point of the approach is a change in the representation of sets. The proposed rep...
DCG
2010
13 years 10 months ago
2010
Given any knot diagram E, we present a sequence of knot diagrams of the same knot type, for which the minimum number of Reidemeister moves required to pass to E is quadratic with ...
DCG
2010
13 years 11 months ago
2010
DCG
2010
13 years 11 months ago
2010
We consider the well known geometric problem of determining shortest paths between pairs of points on a polyhedral surface P, where P consists of triangular faces with positive we...
DCG
2010
13 years 11 months ago
2010
DCG
2010
13 years 11 months ago
2010
The contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we reveal the face structure of the contact polytope of the Leech lattice. We classify i...