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- Konstantin A. Rybnikov
- Discrete & Computational Geometry
- 1999

- Konstantin A. Rybnikov
- ArXiv
- 2003

We show that a PL-realization of a closed connected manifold of dimension n âˆ’ 1 in R (n â‰¥ 3) is the boundary of a convex polyhedron if and only if the interior of each (nâˆ’ 3)-face has a point, whichâ€¦ (More)

We introduce a new class of bootstrap percolation models where the local rules are of a geometric nature as opposed to simple counts of standard bootstrap percolation. Our geometric bootstrapâ€¦ (More)

Georges Voronoi (1908-09) introduced two important reduction methods for positive quadratic forms: the reduction with perfect forms, and the reduction with L-type domains. A form is perfect if it canâ€¦ (More)

- Daniel A. Klain, Konstantin A. Rybnikov, Karen Daniels, Bradford Jones, Cristina Neacsu
- 2005

Determination of the geometry and topology of a 3-dimensional body is an important problem appearing in Computer Aided Design, medical tomography, crystallography, molecular biology, etc. The methodsâ€¦ (More)

- Konstantin A. Rybnikov, Thomas Zaslavsky
- Journal of Graph Theory
- 2006

We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binaryâ€¦ (More)

A polytope D, whose vertices belong to a lattice of rank d, is Delaunay if it can be circumscribed by an ellipsoid E with interior free of lattice points, and so that the vertices of D are the onlyâ€¦ (More)

- Mathieu Dutour, Robert M. Erdahl, Konstantin A. Rybnikov
- 2007

A lattice Delaunay polytope is perfect if its Delaunay sphere is its only circumscribed ellipsoid. A perfect Delaunay polytope naturally corresponds to a positive quadratic function on Z that can beâ€¦ (More)

- Wei Li, Karen Daniels, Konstantin A. Rybnikov
- CCCG
- 2006

A thrackle is a drawing of a simple graph on the plane, where each edge is drawn as a smooth arc with distinct end-points, and every two arcs have exactly one common point, at which they haveâ€¦ (More)

- Konstantin A. Rybnikov, Thomas Zaslavsky
- Discrete & Computational Geometry
- 2005

Consider a gain graph with abelian gain group having no odd torsion. If there is a basis of the graphâ€™s binary cycle space each of whose members can be lifted to a closed walk whose gain is theâ€¦ (More)