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
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
2.
S.S. Akhtamova, V.S. Alekseev, A.P. Lyapin, “$D$-finite Discrete Generating Series and Their Sections”, Mathematics, 13:20 (2025), 3259, 13 pp.
2024
3.
S. S. Akhtamova, T. Cuchta, A. Lyapin, “An Approach to Multidimensional Discrete Generating Series”, Mathematics, 12:1 (2024), 143, 10 pp.
4.
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
5.
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
2023
6.
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
7.
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
8.
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;
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.
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
12.
А. П. Ляпин, Т. Кучта, “Сечения производящего ряда решения разностного уравнения в симплициальном конусе”, Известия Иркутского государственного университета. Серия Математика, 42 (2022), 75–89
2021
13.
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
14.
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
2020
15.
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
16.
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
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
18.
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
2019
19.
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
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
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
2013
22.
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
23.
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
24.
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
25.
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
26.
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
2012
27.
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
2010
28.
A. P. Lyapin, “Ob odnom preobrazovanii kratnogo ryada Lorana”, Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika, 5:18 (2010), 99-108
2009
29.
Evgeny K. Leinartas, Alexander P. Lyapin, “On the Rationality of Multidimentional Recusive Series”, J. Sib. Fed. Univ. Math. Phys., 2:4 (2009), 449–455
30.
Alexander P. Lyapin, “Riordan's Arrays and Two-dimensional Difference Equations”, J. Sib. Fed. Univ. Math. Phys., 2:2 (2009), 210–220
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.
2006
32.
A. P. Lyapin, “Asimptotika koeffitsientov Teilora meromorfnykh funktsii s lineinymi osobennostyami”, Vestnik KrasGU, 6 (2006), 93–97Ssylka na publikatsiyu
2025
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