This article is cited in 3 papers

On the Coprimeness Property of Discrete Systems without the Irreducibility Condition

Masataka Kanki^a, Takafumi Mase^b, Tetsuji Tokihiro<sup>b

a</sup> Department of Mathematics, Kansai University, Japan
^b Graduate School of Mathematical Sciences, University of Tokyo, Japan

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.

MSC: 37K10

Received: April 10, 2018; in final form June 21, 2018; Published online June 27, 2018

Language: English

DOI: 10.3842/SIGMA.2018.065

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