任意维格子上保持互质性的离散 KdV 型方程
Coprimeness-preserving discrete KdV type equation on an arbitrary dimensional lattice
AI总结：
本文提出一个定义在多维格子上的方程，作为保持互质性的类离散KdV方程的扩展及Hietarinta-Viallet方程的高维类似物，主要证明了其tau-function形式的Laurent性质和不可约性质，从而推导出方程的互质性。
摘要：
我们引入一个定义在多维格子上的方程，它可视为我们前一篇论文中保持互质性的类离散 KdV 方程的扩展。该方程也被解释为 Hietarinta-Viallet 方程的高维类似物，后者以其奇点 confinement 性质和指数级次数增长而闻名。作为主要定理，我们证明了该方程在其“tau-function”形式下的 Laurent 性质和不可约性质。由此定理可推导出该方程的互质性。在附录中，我们回顾了作为我们主系统基础方程的保持互质性的类离散 KdV 方程，并证明了诸如互质性等性质。
英文摘要：
We introduce an equation defined on a multi-dimensional lattice, which can be considered as an extension to the coprimeness-preserving discrete KdV like equation in our previous paper. The equation is also interpreted as a higher-dimensional analogue of the Hietarinta-Viallet equation, which is famous for its singularity confining property while having an exponential degree growth. As the main theorem we prove the Laurent and the irreducibility properties of the equation in its "tau-function" form. From the theorem the coprimeness of the equation follows. In Appendix we review the coprimeness-preserving discrete KdV like equation whichis a base equation for our main system and prove the properties such as the coprimeness.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
