4 citations · 7 across the 10 of their papers we have counts for
10 papers
Wug-snake graphs and Markov numbers of matrix semigroups
Oleg Karpenkov, Yefei Ma
Classically, Markov numbers are recovered as perfect matching numbers of domino snake graphs. We extend this correspondence by introducing weighted universal generalised snake grap…
Classifying integer tilings and hypertilings
Oleg Karpenkov, Ian Short, Matty van Son +1
There are two objectives to this work: to classify all tame integer tilings and to classify all tame integer hypertilings. Motivation for the first objective comes from Conway and…
On Euclidean Algorithms for oriented linear Grassmanians
Maxim Arnold, Oleg Karpenkov
In this paper we study Euclidean algorithms and the corresponding continued fractions for oriented linear Grassmanians . We propose two algorithms: Maximal Element Eliminat…
Liftings of surfaces in the plane
Oleg Karpenkov, Brigitte Servatius, Herman Servatius
In this note we provide a topological definition of Maxwell-Cremona liftings for non-planar frameworks of surfaces (both oriented and non-oriented). In the non-oriented case we giv…
Geometry of multidimensional Farey summation algorithm and frieze patterns
Oleg Karpenkov, Matty van Son
In this paper we develop a new geometric approach to subtractive continued fraction algorithms in high dimensions. We adapt a version of Farey summation to the geometric techniques…
On determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators
O. Karpenkov
For a given sequence of positive integers we make an explicit construction of a reduced hyperbolic operator in SL(2,z) with the sequence as a period of a geometric continued fracti…