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
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
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, “Analogs of recurrent Newton formulas”, Russian Math. (Iz. VUZ), 53:10 (2009), 34–44
4.
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
A. A. Kytmanov, “An analog of the Fubini–Studi form for two-dimensional toric varieties”, Siberian Math. J., 44:2 (2003), 286–297
6.
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, “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
8.
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
9.
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
10.
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
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, 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.
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, 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
16.
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, 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
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, “Algorithm of Construction of an Integral Representation Given Toric Variety Fan”, J. Math. Sci., 186:3 (2012), 453–460
20.
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
21.
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
22.
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
23.
V. I. Kuzovatov, A. A. Kytmanov, “Algorithm for Constructing an Analog of Plan’s Formula”, Programming and Computer Software, 44:2 (2018), 100–104
24.
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.V. Shchuplev, “An algorithm for constructing toric compactifications”, Programming and Computer Software, 39:4 (2013), 207–211
26.
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
27.
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
28.
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
29.
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
30.
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
31.
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
32.
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
33.
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
34.
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
35.
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
36.
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
37.
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
38.
M. M. Kucherov, A. A. Kytmanov, “Multivalued logic in the enterprise information management system”, Prikl. Diskr. Mat., 2009, no. supplement № 1, 46–48
39.
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”, Sibirsk. Mat. Zh., 65:1 (2024), 115–124