3 papers
math.CO2008
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…
math.CO2006
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…
math-ph2005
Mobius energy of graphs
Oleg Karpenkov
In the present paper we introduce Mobius energy for the embedded graphs and formulate its main properties. This energy is invariant under the action of the group generated by all i…