The methods of the theory function of several complex variable in the combinatorial analysis.
Main publications:
A.P. Lyapin, S. Chandragiri, “Generating functions for vector partition functions and a basic recurrence relation”, Journal of Difference Equations and Applications, 25:7 (2019), 1052–1061
A. Lyapin, T. Cuchta, “Sections of a generating series of a solution to a difference equation in a simplicial cone”, The Bulletin of Irkutsk State University. Series Mathematics, 2022, no. 42, 75–89
S.S. Akhtamova, T. Cuchta, A. Lyapin, “An Approach to Multidimensional Discrete Generating Series”, Mathematics, 12:1 (2024), 143, 10 с.
A.P. Lyapin, E.N. Mikhalkin, “Algorithm for Finding Singular Points of a General Algebraic Hypersurface”, Programming and Computer Software, 51:2 (2025), 88–92
Evgeny K. Leinartas, Alexander P. Lyapin, “On the Rationality of Multidimentional Recusive Series”, J. Sib. Fed. Univ. Math. Phys., 2:4 (2009), 449–455
2.
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
A. P. Lyapin, S. S. Akhtamova, “Recurrence relations for the sections of the generating series of the solution to the multidimensional difference equation”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:3 (2021), 414–423
4.
A. P. Lyapin, S. Chandragiri, “Generating functions for vector partition functions and a basic recurrence relation”, Journal of Difference Equations and Applications, 25:7 (2019), 1052–1061, arXiv: 1907.12073
А. П. Ляпин, Т. Кучта, “Сечения производящего ряда решения разностного уравнения в симплициальном конусе”, Известия Иркутского государственного университета. Серия Математика, 42 (2022), 75–89
6.
Alexander P. Lyapin, Sreelatha Chandragiri, “The Cauchy problem for multidimensional difference equations in lattice cones”, Zhurn. SFU. Ser. Matem. i fiz., 13:2 (2020), 187–196
M. S. Apanovich, A. P. Lyapin, K. V. Shadrin, “Solving the Cauchy Problem for a Two-Dimensional Difference Equation at a Point Using Computer Algebra Methods”, Programming and Computer Software, 47:1 (2021), 1-5
8.
A. P. Lyapin, E. N. Mikhalkin, “Algorithm for Computing the Truncation of the Discriminant of a Polynomial”, Programming and Computer Software, 49:1 (2023), 49–53
M. S. Apanovich, A. P. :Lyapin, K. V. Shadrin, “Algorithm for Solving the Cauchy Problem for a Two-Dimensional
Difference Equation with Initial Data Defined in a “Strip””, Programming and Computer Software, 48:4 (2022), 286–292
11.
Alexander P. Lyapin, “Riordan's Arrays and Two-dimensional Difference Equations”, J. Sib. Fed. Univ. Math. Phys., 2:2 (2009), 210–220
12.
M. S. Apanovich, A. P. :Lyapin, K. V. Shadrin, “Solving the Cauchy Problem for a Three-dimensional Difference
Equation in a Parallelepiped”, Programming and Computer Software, 49:2 (2023), 61–68
13.
M. S. Apanovich, A. P. Lyapin, K. V. Shadrin, “Calculating the sequence of main minors of the Toeplitz band matrix”, Applied Mathematics & Physics, 52:1 (2020), 5-10
14.
A. P. Lyapin, E. N. Mikhalkin, “Algorithm for Finding Singular Points of a General Algebraic Hypersurface”, Programming and Computer Software, 51:2 (2025), 88–92
15.
S.S. Akhtamova, V.S. Alekseev, A.P. Lyapin, “$D$-finite Discrete Generating Series and Their Sections”, Mathematics, 13:20 (2025), 3259, 13 pp.
16.
S. S. Akhtamova, T. Cuchta, A. Lyapin, “An Approach to Multidimensional Discrete Generating Series”, Mathematics, 12:1 (2024), 143, 10 pp.
17.
A. A. Grigorev, E. K. Leinartas, A. P. Lyapin, “Polinomialnye resheniya mnogomernykh raznostnykh uravnenii”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Materialy 22-i mezhdunarodnoi Saratovskoi zimnei shkoly, posvyaschennoi 300-letiyu RAN. (Saratov, 28–31 yanvarya 2024 g.), Saratovskii natsionalnyi issledovatelskii gosudarstvennyi universitet, 2024, 77–80
18.
A. B. Leinartene, A. P. Lyapin, “Applying Computer Algebra Systems to Study Chaundy-Bullard Identities for the Vector Partition Function with Weight”, Programming and Computer Software, 50:2 (2024), 176–179
19.
Andrey A. Grigoriev, Evgeniy K. Leinartas, Alexander P. Lyapin, “Summation of functions and polynomial solutions to a multidimensional difference equation”, Zhurn. SFU. Ser. Matem. i fiz., 16:2 (2023), 153–161;
20.
A. A. Grigorev, E. K. Leinartas, A. P. Lyapin, “Diskretnyi analog formuly Nyutona-Leibnitsa i operatory s summiruyuschim effektom”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Materialy 21-i mezhdunarodnoi Saratovskoi zimnei shkoly. Saratov, 2022 (Saratov, 31 yanvarya – 04 fevralya 2022 goda), eds. A.P. Khromov (glav. redaktor) [i dr.]., Saratovskii natsionalnyi issledovatelskii gosudarstvennyi universitet imeni N.G. Chernyshevskogo, Saratov, 2022, 118-121
21.
C. C. Akhtamova, V. Yu. Grishunov, A. P. Lyapin, S. A. Tikhomirov, “O secheniyakh proizvodyaschikh ryadov v zadachakh o reshetochnykh putyakh”, Prikladnaya matematika & fizika, 52:2 (2020), 146-151
22.
S. Chandragiri, A. P. Lyapin, “On fundamental solutions to difference equations in lattice cones”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Materialy 20-i mezhdunarodnoi Saratovskoi zimnei shkoly. (Saratov, 28 yanvarya – 01 fevralya 2020 goda), eds. A.P. Khromov (gl. redaktor), B.S. Kashin (zam. gl. redaktora), Yu.S. Kruss (otv. sekretar) [i dr.]., Saratovskii natsionalnyi issledovatelskii gosudarstvennyi universitet imeni N.G. Chernyshevskogo, Saratov, 2020, 449-452
23.
S. A. Tikhomirov, A. P. Lyapin, “O stabilnykh 2-rassloeniyakh s klassami Cherna s1 = 0, s2 = 12 i c2 = 13 na kompleksnom proektivnom prostranstve”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika, 36:19 (2014), 105–111
24.
S. A. Tikhomirov, A. P. Lyapin, V. M. Rostov, “Kombinirovannyi vychislitelnyi metod v sravnitelnom analize komponent Khartskhorna i Vedernikova stabilnykh 2-rassloenii na kompleksnom proektivnom prostranstve”, Yaroslavskii pedagogicheskii vestnik, 3:4 (2013), 12–19
25.
S. A. Tikhomirov, A. P. Lyapin, E. V. Kazantseva, “Spektry stabilnykh 2-rassloenii s nechetnym pervym klassom Cherna na trekhmernom proektivnom prostranstve”, Yaroslavskii pedagogicheskii vestnik, 3:4 (2013), 21–23
26.
S. A. Tikhomirov, A. P. Lyapin, O. A. Voilokova, “Invarianty stabilnykh 2-rassloenii na kompleksnom proektivnom prostranstve i adaptatsiya vychislitelnoi tekhnologii Barta”, Yaroslavskii pedagogicheskii vestnik, 3:2 (2013), 33–38
27.
S. A. Tikhomirov, A. A. Kytmanov, N. N. Osipov, T. L. Troshina, A. P. Lyapin, “O mnogoobrazii modulei M p 3 (2;0,15) stabilnykh 2-rassloenii s klassami Cherna s ;=0 i s 2=15 na kompleksnom proektivnom prostranstve”, Yaroslavskii pedagogicheskii vestnik, 3:4 (2013), 50–55
28.
S. A. Tikhomirov, A. P. Lyapin, A. V. Zhigareva, “Mnogoobraziya modulei stabilnykh refleksivnykh puchkov ranga 2 s nechetnym pervym klassom Cherna na kompleksnom proektivnom prostranstve”, Yaroslavskii pedagogicheskii vestnik, 3:3 (2013), 68–74
29.
S. A. Tikhomirov, A. P. Lyapin, E. A. Ruzanov, “O mnogoobraziyakh modulei M p3 (2;0,10) i M p3 (2;0,11) stabilnykh 2-rassloenii s klassami Cherna c 1 = 0, c 2 = 10 i 11 na kompleksnom proektivnom prostranstve”, Yaroslavskii pedagogicheskii vestnik, 3:4 (2012), 13–18
30.
A. P. Lyapin, “Ob odnom preobrazovanii kratnogo ryada Lorana”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika, 5:18 (2010), 99-108
31.
A. P. Lyapin, O ratsionalnosti z-preobrazovaniya reshenii mnogomernykh raznostnykh uravnenii i ikh asimptotike, Diss. … kand. fiz.-matem. nauk, SFU, Krasnoyarsk, 2009, 78 pp.
32.
A. P. Lyapin, “Asimptotika koeffitsientov Teilora meromorfnykh funktsii s lineinymi osobennostyami”, Vestnik KrasGU, 6 (2006), 93–97Ssylka na publikatsiyu
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