11 citations · 43 across the 30 of their papers we have counts for
8 papers · 1 filter
D Farey graph, lambda lengths and -tilings
Anna Felikson, Oleg Karpenkov, Khrystyna Serhiyenko +1
We explore a three-dimensional counterpart of the Farey tessellation and its relations to Penner's lambda lengths and -tilings. In particular, we prove a three-dimensional ve…
Geometric criteria for realizability of tensegrities in higher dimensions
Oleg Karpenkov, Christian Müller
In this paper we study a classical Maxwell question on the existence of self-stresses for frameworks, which are called tensegrities. We give a complete answer on geometric conditio…
Tensegrities on the space of generic functions
Oleg Karpenkov
In this small note we introduce a notion of self-stresses on the set functions in two variables with generic critical points. The notion naturally comes from a rather exotic repres…
On stratifications for planar tensegrities with a small number of vertices
Oleg Karpenkov, Jan Schepers, Brigitte Servatius
In this paper we discuss several results about the structure of the configuration space of two-dimensional tensegrities with a small number of points. We briefly describe the techn…
Geometry of configuration spaces of tensegrities
Franck Doray, Oleg Karpenkov, Jan Schepers
Consider a graph G with n vertices. In this paper we study geometric conditions for an n-tuple of points in R^d to admit a tensegrity with underlying graph G. We introduce and inve…
On examples of difference operators for -valued functions over finite sets
Oleg Karpenkov
Recently V.I.Arnold have formulated a geometrical concept of monads and apply it to the study of difference operators on the sets of -valued sequences of length . In th…
Elementary notions of lattice trigonometry
Oleg Karpenkov
In this paper we study properties of lattice trigonometric functions of lattice angles in lattice geometry. We introduce the definition of sums of lattice angles and establish a ne…
Classification of lattice-regular lattice convex polytopes
Oleg Karpenkov
In this paper for any dimension n we give a complete list of lattice convex polytopes in R^n that are regular with respect to the group of affine transformations preserving the lat…