On the Coprimeness Property of Discrete Systems without the Irreducibility Condition
In this article, we investigate the coprimeness properties of one and two-dimensional discrete equations in a situation where the equations are decomposable into several factors of polynomials. After experimenting on a simple equation, we shall focus on some higher power extensions of the Somos-4 eq...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209785 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the Coprimeness Property of Discrete Systems without the Irreducibility Condition / M. Kanki, T. Mase, T. Tokihiro // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862642022817464320 |
|---|---|
| author | Kanki, M. Mase, T. Tokihiro, T. |
| author_facet | Kanki, M. Mase, T. Tokihiro, T. |
| citation_txt | On the Coprimeness Property of Discrete Systems without the Irreducibility Condition / M. Kanki, T. Mase, T. Tokihiro // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this article, we investigate the coprimeness properties of one and two-dimensional discrete equations in a situation where the equations are decomposable into several factors of polynomials. After experimenting on a simple equation, we shall focus on some higher power extensions of the Somos-4 equation and the (1-dimensional) discrete Toda equation. Our previous results are that all of the equations satisfy the irreducibility and the coprimeness properties if the r.h.s. is not factorizable. In this paper, we shall prove that the coprimeness property still holds for all of these equations, even if the r.h.s. is factorizable, although the irreducibility property is no longer satisfied.
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| first_indexed | 2025-12-07T14:17:03Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209785 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T14:17:03Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kanki, M. Mase, T. Tokihiro, T. 2025-11-26T12:23:10Z 2018 On the Coprimeness Property of Discrete Systems without the Irreducibility Condition / M. Kanki, T. Mase, T. Tokihiro // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10 arXiv: 1804.02804 https://nasplib.isofts.kiev.ua/handle/123456789/209785 https://doi.org/10.3842/SIGMA.2018.065 In this article, we investigate the coprimeness properties of one and two-dimensional discrete equations in a situation where the equations are decomposable into several factors of polynomials. After experimenting on a simple equation, we shall focus on some higher power extensions of the Somos-4 equation and the (1-dimensional) discrete Toda equation. Our previous results are that all of the equations satisfy the irreducibility and the coprimeness properties if the r.h.s. is not factorizable. In this paper, we shall prove that the coprimeness property still holds for all of these equations, even if the r.h.s. is factorizable, although the irreducibility property is no longer satisfied. We thank the referees for reminding us of several important papers regarding the Laurent systems and the discrete integrability. We acknowledge support from KAKENHI Grant numbers 26400109, 16H06711, and 17K14211. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Coprimeness Property of Discrete Systems without the Irreducibility Condition Article published earlier |
| spellingShingle | On the Coprimeness Property of Discrete Systems without the Irreducibility Condition Kanki, M. Mase, T. Tokihiro, T. |
| title | On the Coprimeness Property of Discrete Systems without the Irreducibility Condition |
| title_full | On the Coprimeness Property of Discrete Systems without the Irreducibility Condition |
| title_fullStr | On the Coprimeness Property of Discrete Systems without the Irreducibility Condition |
| title_full_unstemmed | On the Coprimeness Property of Discrete Systems without the Irreducibility Condition |
| title_short | On the Coprimeness Property of Discrete Systems without the Irreducibility Condition |
| title_sort | on the coprimeness property of discrete systems without the irreducibility condition |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209785 |
| work_keys_str_mv | AT kankim onthecoprimenesspropertyofdiscretesystemswithouttheirreducibilitycondition AT maset onthecoprimenesspropertyofdiscretesystemswithouttheirreducibilitycondition AT tokihirot onthecoprimenesspropertyofdiscretesystemswithouttheirreducibilitycondition |