Publications
Selected publications
- Geometry and combinatoric of Minkowski-Voronoi 3-dimensional continued fractions (Journal article - 2014)
2024
On a periodic Jacobi-Perron type algorithm
Karpenkov, O. (n.d.). On a periodic Jacobi-Perron type algorithm. Monatshefte für Mathematik. doi:10.1007/s00605-024-02006-5
2023
Multidimensional integer trigonometry
Blackman, J., Dolan, J., & Karpenkov, O. (n.d.). Multidimensional integer trigonometry. Communications in Mathematics, Volume 31 (2023), Issue 2.... doi:10.46298/cm.10919
2022
On Hermite's problem, Jacobi-Perron type algorithms, and Dirichlet groups
Karpenkov, O. (2022). On Hermite's problem, Jacobi-Perron type algorithms, and Dirichlet groups. ACTA ARITHMETICA, 203(1), 27-48. doi:10.4064/aa210614-5-1
Geometry of Continued Fractions
Karpenkov, O. N. (2022). Geometry of Continued Fractions. Springer Berlin Heidelberg. doi:10.1007/978-3-662-65277-0
2021
Continued Fraction approach to Gauss Reduction Theory
Karpenkov, O. (2021). Continued Fraction approach to Gauss Reduction Theory. In International Conference on Reachability Problems. doi:10.1007/978-3-030-89716-1_7
2020
Equilibrium stressability of multidimensional frameworks
Karpenkov, O., Müller, C., Panina, G., Servatius, B., Servatius, H., & Siersma, D. (2020). Equilibrium stressability of multidimensional frameworks. Retrieved from http://arxiv.org/abs/2009.05469v1
Equilibrium stressability of multidimensional frameworks
Equilibrium stressability of multidimensional frameworks
Karpenkov, O., Müller, C., Panina, G., Servatius, B., Servatius, H., & Siersma, D. (2022). Equilibrium stressability of multidimensional frameworks. European Journal of Mathematics. doi:10.1007/s40879-021-00523-3
Generalised Markov numbers
Karpenkov, O., & van-Son, M. (2020). Generalised Markov numbers. Journal of Number Theory, 213, 16-66. doi:10.1016/j.jnt.2020.01.010
2019
Martin Integral Representation for Nonharmonic Functions and Discrete Co-Pizzetti Series
Boiko, T., & Karpenkov, O. (2019). Martin Integral Representation for Nonharmonic Functions and Discrete Co-Pizzetti Series. MATHEMATICAL NOTES, 106(5-6), 659-673. doi:10.1134/S0001434619110014
The Sixth International Conference on Uniform Distribution Theory (UDT 2018) CIRM, Luminy, Marseilles, France, October 1–5, 2018.
Nair, R., Karpenkov, O., & Verger-Gaugry, J. -L. (2019). The Sixth International Conference on Uniform Distribution Theory (UDT 2018) CIRM, Luminy, Marseilles, France, October 1–5, 2018.. Uniform Distribution Theory. doi:10.2478/UDT-2019–0009
Generalized Perron Identity for broken lines
Karpenkov, O., & Van-Son, M. (2019). Generalized Perron Identity for broken lines. JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 31(1), 131-144. Retrieved from http://gateway.webofknowledge.com/
Generalized Perron Identity for broken lines
Karpenkov, O., & van-Son, M. (2019). Generalized Perron Identity for broken lines. Journal de Theorie des Nombres de Bordeaux, 31(1), 131-144. doi:10.5802/jtnb.1071
Geometric criteria for realizability of tensegrities in higher dimensions
Karpenkov, O., & Müller, C. (n.d.). Geometric criteria for realizability of tensegrities in higher dimensions. Retrieved from http://arxiv.org/abs/1907.02830v2
Geometric criteria for realizability of tensegrities in higher dimensions
Karpenkov, O., & Mueller, C. (2021). GEOMETRIC CRITERIA FOR REALIZABILITY OF TENSEGRITIES IN HIGHER DIMENSIONS. SIAM JOURNAL ON DISCRETE MATHEMATICS, 35(2), 637-660. doi:10.1137/19M1281903
Tensegrities on the space of generic functions
Karpenkov, O. (2019). Tensegrities on the space of generic functions. Retrieved from http://arxiv.org/abs/1905.11262v1
2018
On Periodic Asymmetric Extrapolation
Boiko, T., Karpenkov, O., & Rakhimberdiev, B. (2018). On Periodic Asymmetric Extrapolation. MATHEMATICAL NOTES, 104(5-6), 642-654. doi:10.1134/S0001434618110044
Generalised Markov numbers
Geometric Conditions of Rigidity in Nongeneric settings
Karpenkov, O. (2018). Geometric Conditions of Rigidity in Nongeneric settings. In J. Sidman, A. S. John, & M. Sitharam (Eds.), Handbook of Geometric Constraint Systems Principles. CRC Press.
Open Problems on Configuration Spaces of Tensegrities
Karpenkov, O. (2018). Open Problems on Configuration Spaces of Tensegrities. Arnold Mathematical Journal, 4(1), 19-25. doi:10.1007/s40598-018-0080-7
2017
Open problems in geometry of continued fractions
Karpenkov, O. (2017). Open problems in geometry of continued fractions. Retrieved from http://arxiv.org/abs/1712.01450v1
Forecasting Algorithms for Recurrent Patterns in Consumer Demand
Perron identity for arbitrary broken lines
ALEXEI BRONISLAVOVICH SOSSINSKY TURNS 80
Chernavski, A., Fuchs, D., Gussein-Zade, S., Ilyashenko, Y., Karpenkov, O., Kirillov, A., . . . Vassiliev, V. (2017). ALEXEI BRONISLAVOVICH SOSSINSKY TURNS 80. MOSCOW MATHEMATICAL JOURNAL, 17(3), 555-558. Retrieved from https://www.webofscience.com/
2015
The combinatorial geometry of stresses in frameworks
Karpenkov, O. (n.d.). The combinatorial geometry of stresses in frameworks. Discrete and Computational Geometry: an international journal of mathematics and computer science. doi:10.1007/s00454-020-00234-8
2014
Geometry and combinatoric of Minkowski--Voronoi 3-dimesional continued fractions
Geometry and combinatoric of Minkowski-Voronoi 3-dimensional continued fractions
Karpenkov, O., & Ustinov, A. (2017). Geometry and combinatoric of Minkowski-Voronoi 3-dimensional continued fractions. Journal of Number Theory, 176, 375-419. doi:10.1016/j.jnt.2016.12.005
On offsets and curvatures for discrete and semidiscrete surfaces
Karpenkov, O., & Wallner, J. (2014). On offsets and curvatures for discrete and semidiscrete surfaces. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 55(1), 207-228. doi:10.1007/s13366-013-0146-6
2013
Mean value property for nonharmonic functions
Boiko, T., & Karpenkov, O. (2013). Mean value property for nonharmonic functions. Retrieved from http://arxiv.org/abs/1309.5040v1
Mean value property for nonharmonic functions
Euler elasticae in the plane and the Whitney--Graustein theorem
Avvakumov, S., Karpenkov, O., & Sossinsky, A. (2013). Euler elasticae in the plane and the Whitney--Graustein theorem. Retrieved from http://dx.doi.org/10.1134/S1061920813030011
Euler elasticae in the plane and the Whitney--Graustein theorem
Geometry of Continued Fractions
Karpenkov, O. (2013). Geometry of Continued Fractions. Springer Berlin Heidelberg. doi:10.1007/978-3-642-39368-6
On stratifications for planar tensegrities with a small number of vertices
Karpenkov, O., Schepers, J., & Servatius, B. (n.d.). On stratifications for planar tensegrities with a small number of vertices. Ars Mathematica Contemporanea, 6(2), 305-322. doi:10.26493/1855-3974.299.678
2012
On Asymptotic Reducibility in SL(3,Z)
Karpenkov, O. (2012). On Asymptotic Reducibility in SL(3,Z). Retrieved from http://arxiv.org/abs/1205.4166v1
On stratifications for planar tensegrities with a small number of vertices
Karpenkov, O., Schepers, J., & Servatius, B. (2012). On stratifications for planar tensegrities with a small number of vertices. Retrieved from http://arxiv.org/abs/1201.3557v1
On stratifications for planar tensegrities with a small number of vertices
2011
Energies of knot diagrams
Energies of knot diagrams
Karpenkov, O., & Sossinsky, A. (2011). Energies of knot diagrams. Retrieved from http://dx.doi.org/10.1134/S1061920811030046
2010
Vladimir Igorevich Arnold
Karpenkov, O. (2010). Vladimir Igorevich Arnold. Internat. Math. Nachrichten, 2010. Retrieved from http://arxiv.org/abs/1007.0688v1
Finite and infinitesimal flexibility of semidiscrete surfaces
Karpenkov, O. (2015). Finite and infinitesimal flexibility of semidiscrete surfaces. Arnold Mathematical Journal, 1(04), 403-444. doi:10.1007/s40598-015-0025-3
2009
On tori triangulations associated with two-dimensional continued fractions of cubic irrationalities
Karpenkov, O. (2009). On tori triangulations associated with two-dimensional continued fractions of cubic irrationalities. Funktsional. Anal. i Prilozhen. 38 (2004), no. 2, 28--37, 95; translation in Funct. Anal. Appl. 38 (2004), no. 2, 102--110. Retrieved from http://dx.doi.org/10.1023/B:FAIA.0000034040.08573.22
On two-dimensional continued fractions for the integer hyperbolic matrices with small norm
Karpenkov, O. (2009). On two-dimensional continued fractions for the integer hyperbolic matrices with small norm. Uspekhi Mat. Nauk 59 (2004), no. 5(359), 149--150; translation in Russian Math. Surveys 59 (2004), no. 5, 959--960. Retrieved from http://dx.doi.org/10.1070/RM2004v059n05ABEH000778
Continued fractions and the second Kepler law
Karpenkov, O. (2009). Continued fractions and the second Kepler law. Retrieved from http://arxiv.org/abs/0911.2791v1
Bernoulli-Euler numbers and multiboundary singularities of type $B_n^l$
Karpenkov, O. (2009). Bernoulli-Euler numbers and multiboundary singularities of type $B_n^l$. Retrieved from http://arxiv.org/abs/0910.4046v1
Rational approximation of the maximal commutative subgroups of GL(n,R)
Karpenkov, O., & Vershik, A. (2009). Rational approximation of the maximal commutative subgroups of GL(n,R). Retrieved from http://arxiv.org/abs/0910.3482v1
On irrational lattice angles
Karpenkov, O. (2009). On irrational lattice angles. Functional Analysis and Other Mathematics, 2(2-4), 221-239. doi:10.1007/s11853-008-0029-9
2008
On the flexibility of Kokotsakis meshes
Karpenkov, O. (2008). On the flexibility of Kokotsakis meshes. Retrieved from http://arxiv.org/abs/0812.3050v1
Geometry of configuration spaces of tensegrities
Doray, F., Karpenkov, O., & Schepers, J. (2008). Geometry of configuration spaces of tensegrities. Retrieved from http://arxiv.org/abs/0806.4976v2
Geometry of configuration spaces of tensegrities
Elementary notions of lattice trigonometry
Karpenkov, O. (n.d.). Elementary notions of lattice trigonometry. MATHEMATICA SCANDINAVICA, 102(2), 161. doi:10.7146/math.scand.a-15058
2007
Multidimensional Gauss Reduction Theory for conjugacy classes of SL(n,Z)
Karpenkov, O. (2007). Multidimensional Gauss Reduction Theory for conjugacy classes of SL(n,Z). Retrieved from http://arxiv.org/abs/0711.0830v3
On determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators
Karpenkov, O. (2007). On determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators. Retrieved from http://arxiv.org/abs/0708.1604v1
2006
On existence and uniqueness conditions for an integer triangle with given angles
Karpenkov, O. N. (2006). On existence and uniqueness conditions for an integer triangle with given angles. Russian Mathematical Surveys, 61(6), 1178-1179. doi:10.1070/rm2006v061n06abeh004374
On examples of difference operators for $\{0,1\}$-valued functions over finite sets
Karpenkov, O. (2006). On examples of difference operators for $\{0,1\}$-valued functions over finite sets. Functional Analysis and Other Mathematics,vol.1(2), pp.197-202, 2006. Retrieved from http://dx.doi.org/10.1007/s11853-007-0010-z
Approximating reals by rationals of the form a/b^2
Karpenkov, O. (2006). Approximating reals by rationals of the form a/b^2. Retrieved from http://arxiv.org/abs/math/0610717v2
On invariant Mobius measure and Gauss-Kuzmin face distribution
Karpenkov, O. (2006). On invariant Mobius measure and Gauss-Kuzmin face distribution. Proceedings of the Steklov Institute of Mathematics, vol.258, pp.74-86, 2007. Retrieved from http://arxiv.org/abs/math/0610042v2
Elementary notions of lattice trigonometry
Karpenkov, O. (2006). Elementary notions of lattice trigonometry. 2008. The second part in Funct. Anal. Other Math., 2, 2-4. Retrieved from http://arxiv.org/abs/math/0604129v3
Combinatorics of multiboundary singularities B_n^l and Bernoulli-Euler numbers
Karpenkov, O. (2006). Combinatorics of multiboundary singularities B_n^l and Bernoulli-Euler numbers. Funct. Anal. Appl. 36(2002), no 1, 78-81. Retrieved from http://arxiv.org/abs/math/0604024v1
Classification of lattice-regular lattice convex polytopes
Karpenkov, O. (2006). Classification of lattice-regular lattice convex polytopes. Functional Analysis and Other Mathematics, vol.1(1), pp.17-35, 2006. Retrieved from http://dx.doi.org/10.1007/s11853-007-0002-z
Three examples of three-dimensional continued fractions in the sense of Klein
Karpenkov, O. (2006). Three examples of three-dimensional continued fractions in the sense of Klein. C. R. Acad. Sci. Paris, Ser.I 343, pp.5-7, 2006. Retrieved from http://arxiv.org/abs/math/0601493v1
2005
Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions
Karpenkov, O. (2005). Completely empty pyramids on integer lattices and two-dimensional faces of multidimensional continued fractions. Monatshefte fuer Mathematik, 152, 217-249. Retrieved from http://arxiv.org/abs/math/0510482v2
Mobius energy of graphs
Karpenkov, O. (2005). Mobius energy of graphs. Math. Notes, vol. 79(2006), no.1, pp.134--138.. Retrieved from http://arxiv.org/abs/math-ph/0509055v1
Classification of three-dimensional multistorey completely empty convex marked pyramids
Karpenkov, O. N. (2005). Classification of three-dimensional multistorey completely empty convex marked pyramids. Russian Mathematical Surveys, 60(1), 165-166. doi:10.1070/rm2005v060n01abeh000816
2004
Energy of a knot: variational principles; Mm-energy
Karpenkov, O. N. (2004). Energy of a knot: variational principles; Mm-energy. Fund. Math. Today, 214-223. Retrieved from http://arxiv.org/abs/math/0411060v1
On examples of two-dimensional periodic continued fractions
Karpenkov, O. N. (2004). On examples of two-dimensional periodic continued fractions. Retrieved from http://arxiv.org/abs/math/0411054v1
Constructing multidimensional periodic continued fractions in the sense of Klein
Karpenkov, O. (2004). Constructing multidimensional periodic continued fractions in the sense of Klein. Retrieved from http://arxiv.org/abs/math/0411031v3
2003
'Energy of a knot: some new aspects'
Karpenkov, O. (2003). 'Energy of a knot: some new aspects'. Fundamental mathematics today, 214-223.
2002
Energy of a knot: Variational principles
Karpenkov, O. (2002). Energy of a knot: Variational principles. Russian Journal of Mathematical Physics, 9(3), 275-287.
Karpenkov, O. N. (2002). Unknown Title. Functional Analysis and Its Applications, 36(1), 65-67. doi:10.1023/a:1014434318546