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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 065, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.065 (Mi sigma1364) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the Coprimeness Property of Discrete Systems without the Irreducibility Condition

Masataka Kankia, Takafumi Maseb, Tetsuji Tokihirob

a Department of Mathematics, Kansai University, Japan
b Graduate School of Mathematical Sciences, University of Tokyo, Japan
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DOI: https://doi.org/10.3842/SIGMA.2018.065
Abstract: 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.
Keywords: integrability detector; coprimeness; singularity confinement; discrete Toda equation.
Funding agency Grant number
Japan Society for the Promotion of Science 26400109
16H06711
17K14211
We acknowledge support from KAKENHI Grant numbers 26400109, 16H06711 and 17K14211.
Received: April 10, 2018; in final form June 21, 2018; Published online June 27, 2018
Bibliographic databases:
Document Type: Article
MSC: 37K10
Language: English
Citation: Masataka Kanki, Takafumi Mase, Tetsuji Tokihiro, “On the Coprimeness Property of Discrete Systems without the Irreducibility Condition”, SIGMA, 14 (2018), 065, 17 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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