Computer Algebra, Several Complex Variables, Algebraic Geometry.
Main publications:
A. A. Kytmanov, “An analog of the Fubini-Studi form for two-dimensional toric varieties”, Siberian Mathematical Journal, 44:2 (2003), 286–297
A. A. Kytmanov, A. Y. Semusheva, “Averaging of the Cauchy kernels and integral realization of the local residue”, Mathematische Zeitschrift, 264:1 (2010), 87–98
A. A. Kytmanov, A. M. Kytmanov, E. K. Myshkina, “Finding residue integrals for systems of non-algebraic equations in $\mathbb{C}^n$”, Journal of Symbolic Computation, 66 (2015), 98–110
A. A. Kytmanov, A. M. Kytmanov, E. K. Myshkina, “Residue integrals and Waring’s formulas for algebraic or even transcendental system”, Complex Variables and Elliptic Equations, 64:1 (2019), 93–111
A. A. Kytmanov, A. S. Tikhomirov, S. A. Tikhomirov, “Series of rational moduli components of stable rank two vector bundles on $\mathbb{P}^3$”, Selecta Mathematica New Series, 25:2 (2019), 29
Alexey A. Kytmanov, Sergey A. Tikhomirov, “On the dimensions of components of stable rank $2$ vector bundles with odd determinant on $\mathbb{P}^{3}$”, Zhurn. SFU. Ser. Matem. i fiz., 19:1 (2026), 65–71;
2025
2.
A. A. Kytmanov, N. N. Osipov, S. A. Tikhomirov, “Series of Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on P3”, Siberian Mathematical Journal, 66:1 (2025), 53–63
3.
V. I. Kuzovatov, A. A. Kytmanov, “On the Calculation of the Number of Real Roots of a System of Nonalgebraic Equations Using Computer Algebra”, Programming and Computer Software, 51:2 (2025), 83–87
4.
A. A. Kytmanov, S. P. Tsarev, “Asymptotics of solutions of special second-order linear recurrencies with polynomial coefficients and boundary effects of polynomial filters”, Journal of Symbolic Computation, 128 (2025), 102386, 12 pp.
2024
5.
A. A. Kytmanov, N. N. Osipov, S. A. Tikhomirov, “Two Series of Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on the Projective Space”, Siberian Mathematical Journal, 65:1 (2024), 96–105
6.
V. R. Kulikov, A. A. Kytmanov, A. O. Poroshin, I. V. Timofeev, D. P. Fedchenko, “On Linear Cellular Automata”, Programming and Computer Software, 50:1 (2024), 24–30
7.
V. I. Kuzovatov, A. A. Kytmanov, E. K. Myshkina, “On Calculating Partial Sums of Multiple Numerical Series by Methods of Computer Algebra”, Programming and Computer Software, 50:2 (2024), 172–175
8.
A. A. Kytmanov, S. P. Tsarev, “Discrete orthogonal polynomials: anomalies of time series and boundary effects of polynomial filters”, Kaptsov, O. and Kaptsov, E. ed. Mathematical Models and Integration Methods: Seminar Proceedings on Applications to Mechanics and Physics, Berlin, Boston: De Gruyter, 2024, 143–164
2023
9.
A. A. Kytmanov, N. N. Osipov, S. A. Tikhomirov, “On the number of irreducible components of the moduli space of semistable reflexive rank 2 sheaves on the projective space”, Siberian Mathematical Journal, 64:1 (2023), 103–110
10.
V. I. Kuzovatov, A. A. Kytmanov, E. K. Myshkina, “Symbolic Algorithm for Finding Zeros of a System of Holomorphic Functions”, Programming and Computer Software, 49:2 (2023), 86–90
11.
T. A. Kustitskaya, R. V. Esin, A. A. Kytmanov, T. V. Zykova., “Designing an Education Database in a Higher Education Institution for the Data-Driven Management of the Educational Process”, Education Sciences, 13:9 (2023), 947, 23 pp. Link
A. A. Kytmanov, N. N. Osipov, S. A. Tikhomirov, T. V. Zykova, “On numerical characteristics of some bundles and their isomorphism classes on $\mathbb{P}^3$”, Sib. Èlektron. Mat. Izv., 19:2 (2022), 415–425
13.
T. A. Kustitskaya, A. A. Kytmanov, M. V. Noskov, “Early student-at-risk detection by current learning performance and learning behavior indicators”, Cybernetics and Information Technologies, 22:1 (2022), 117–133
V. I. Kuzovatov, A. A. Kytmanov, E. K. Myshkina, “On Computing the Resultant of a Polynomial and an Entire Function”, Programming and Computer Software, 48:1 (2022), 59–64
15.
R. V. Yesin, T. V. Zykova, T. A. Kustitskaya, A. A. Kytmanov, “Digital educational history as a component of the digital student's profile in the context of education transformati”, Perspektivy Nauki i Obrazovania, 59:5 (2022), 566–584
2021
16.
Osipov, N.N., Kytmanov, A.A., “An Algorithm for Solving a Family of Fourth-Degree Diophantine Equations that Satisfy Runge’s Condition”, Programming and Computer Software, 47:1 (2021), 29–33
17.
Kuzovatov, V.I., Kytmanov, A.A., Myshkina, E.K., “An Algorithm for Constructing the Resultant of Two Entire Functions”, Programming and Computer Software, 47:2 (2021), 139–143
18.
Vokhmin S.A., Kytmanov A.A., Erlykov G.P., Shevnina E.V., Kurchin G.S., Kirsanov A.K., “Prediction and Actual Oversized/Undersized Fragmentation in Underground Blasting”, Journal of Mining Science, 57:2 (2021), 210–219
19.
Osipov, N.N., Kytmanov, A.A., “Simplification of Nested Real Radicals Revisited”, Proceedings of CASC 2021: Computer Algebra in Scientific Computing: 23rd International Workshop, (F. Boulier et al. eds.), Lecture Notes in Computer Science, 12865, Springer International Publishing, 2021, 293–313
2020
20.
Kuzovatov, V.I., Kytmanov, A.A., Kuzovatova, O.I., “Algorithm for constructing an analogue of the Binet formula”, Programming and Computer Software, 46:2 (2020), 105–109
21.
Auzinger, W., Kytmanov, A.A., Tsarev, S.P., “A Study of Anomalies in GPS Time Series via Polynomial Filtering”, 2020 IEEE 15th International Scientific and Technical Conference on Computer Sciences and Information Technologies, CSIT 2020 – Proceedings, IEEE, 2020, 175–178
2019
22.
A. A. Kytmanov, A. M. Kytmanov, E. K. Myshkina, “Residue integrals and Waring’s formulas for algebraic or even transcendental systems”, Complex Variables and Elliptic Equations, 64:1 (2019), 93–111
I. B. Gorshkov, I. Kaygorodov, A. A. Kytmanov, M. A. Salim, “The variety of nilpotent Tortkara algebras”, Zhurn. SFU. Ser. Matem. i fiz., 12:2 (2019), 173–184
A. A. Kytmanov, A. S. Tikhomirov, S. A. Tikhomirov, “Series of rational moduli components of stable rank two vector bundles on $\mathbb{P}^3$”, Selecta Mathematica, New Series, 25:2 (2019), 29, 47 pp.
V. I. Kuzovatov, A. A. Kytmanov, “Algorithm for Constructing an Analog of Plan’s Formula”, Programming and Computer Software, 44:2 (2018), 100–104
26.
M. A. Styugin, A. A. Kytmanov, T. N. Yamskikh, “Formalization of the problem of protection against reconnaissance in conflict systems”, Journal of Discrete Mathematical Sciences and Cryptography, 21:3 (2018), 679–694
A. A. Kytmanov, A. P. Lyapin, T. M. Sadykov, “Evaluating the rational generating function for the solution of the Cauchy problem for a two-dimensional difference equation with constant coefficients”, Programming and Computer Software, 43:2 (2017), 105–111
28.
Kurchin G.S., Vokhmin S.A., Kytmanov, A.A., “Impact of the shape of geological contact on mining losses in the process of near-contact zone development”, Journal of Mining institute, 223 (2017), 37–43
29.
S. A. Vokhmin, A. A. Kytmanov, G. S. Kurchin, Y. P. Trebush, A. K. Kirsanov, “Calculation of loss volumes and dilution of mineral deposits in near-contact zones”, ARPN Journal of Engineering and Applied Sciences, 12:19 (2017), 5447-5456
2016
30.
A. A. Kytmanov, N. N. Osipov, S. A. Tikhomirov, “Finding Ein components in the moduli spaces of stable rank $2$ bundles on the projective $3$-space”, Siberian Math. J., 57:2 (2016), 322–329
31.
A. A. Kytmanov, A. V. Shchuplev, T. V. Zykova, “Algorithm for construction of volume forms on toric varieties starting from a convex integer polytope”, Programming and Computer Software, 42:2 (2016), 99–106
32.
D. V. Bogdanov, A. A. Kytmanov, T. M. Sadykov, “Algorithmic computation of polynomial amoebas”, Proceedings of CASC 2016: Computer Algebra in Scientific Computing: 18th International Workshop, (V.P. Gerdt et al. eds.), Lecture Notes in Computer Science, 9890, Springer International Publishing, 2016, 87–100
A. A. Kytmanov, M. V. Noskov, K. V. Safonov, M. V. Savelyeva, V. A. Shershneva, “Competency-based learning in higher mathematics education as a cluster of efficient approaches”, Bolema - Mathematics Education Bulletin, 30:56 (2016), 1113–1126
M.A. Styugin, A.A. Kytmanov, “Mathematical modeling of user perception in information security systems”, Zhurn. SFU. Ser. Matem. i fiz., 8:4 (2015), 454–466http://elib.sfu-kras.ru/handle/2311/19861
A.A. Kytmanov, A.M. Kytmanov, E.K. Myshkina, “Finding residue integrals for systems of non-algebraic equations in Cn”, Journal of Symbolic Computation, 66 (2015), 98–110
A. A. Kytmanov, A. M. Kytmanov, E. K. Myshkina, “On finding residue integrals for a class of systems of non-algebraic equations”, ACM Communications in Computer Algebra, 49:3 (2015), 77–79
2014
37.
V. I. Kuzovatov, A. A. Kytmanov, “On the zeta-function of zeros of some class of entire functions”, Zhurn. SFU. Ser. Matem. i fiz., 7:4 (2014), 489–499
A.A. Kytmanov, A.V. Shchuplev, “An algorithm for constructing toric compactifications”, Programming and Computer Software, 39:4 (2013), 207–211
2012
39.
A. A. Kytmanov, “Algorithm of Construction of an Integral Representation Given Toric Variety Fan”, J. Math. Sci., 186:3 (2012), 453–460
2010
40.
A.A. Kytmanov, “An algorithm for calculating power sums of roots for a class of systems of nonlinear equations”, Programming and Computer Software, 36:2 (2010), 103–110
41.
A.A. Kytmanov, A.Y. Semusheva, “Averaging of the Cauchy kernels and integral realization of the local residue”, Mathematische Zeitschrift, 264:1 (2010), 87–98
A. A. Kytmanov, “Analogs of recurrent Newton formulas”, Russian Math. (Iz. VUZ), 53:10 (2009), 34–44
43.
M. M. Kucherov, A. A. Kytmanov, “Multivalued logic in the enterprise information management system”, Prikl. Diskr. Mat., 2009, no. supplement № 1, 46–48
2008
44.
Alexey A. Kytmanov, “Integral Representations and Volume Forms on Hirzebruch Surfaces”, Zhurn. SFU. Ser. Matem. i fiz., 1:2 (2008), 125–132
A. A. Kytmanov, “On an analogue of the Bochner–Martinelli representation in $d$-circled polyhedra in the space $\mathbb C^d$”, Russian Math. (Iz. VUZ), 49:3 (2005), 49–55
2003
46.
A. A. Kytmanov, “An analog of the Fubini–Studi form for two-dimensional toric varieties”, Siberian Math. J., 44:2 (2003), 286–297
2026
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