11 citations · 43 across the 30 of their papers we have counts for
33 papers
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…
Multidimensional integer trigonometry
John Blackman, James Dolan, Oleg Karpenkov
This paper is dedicated to providing an introduction into multidimensional integer trigonometry. We start with an exposition of integer trigonometry in two dimensions, which was in…
Continued Fraction approach to Gauss Reduction Theory
Oleg Karpenkov
Jordan Normal Forms serve as excellent representatives of conjugacy classes of matrices over closed fields. Once we knows normal forms, we can compute functions of matrices, their…
On a periodic Jacobi-Perron type algorithm
Oleg Karpenkov
In this paper we introduce a new modification of the Jacobi-Perron algorithm in three dimensional case and prove its periodicity for the case of totally-real conjugate cubic vector…
On Hermite's problem, Jacobi-Perron type algorithms, and Dirichlet groups
Oleg Karpenkov
In 1848 Ch.~Hermite asked if there exists some way to write cubic irrationalities periodically. A little later in order to approach the problem C.G.J.~Jacobi and O.~Perron generali…
Equilibrium stressability of multidimensional frameworks
Oleg Karpenkov, Christian Müller, Gaiane Panina +3
We prove an equilibrium stressability criterium for trivalent multidimensional tensegrities. The criterium appears in different languages: (1) in terms of stress monodromies, (2) i…