$ε$ - BBS和Schensted插入算法的推广
Generalization of the $ε$-BBS and the Schensted insertion algorithm
摘要：
$ε$ -BBS是通过对基本Toda轨道进行超离散化而得到的孤子元胞自动机族，它是统一Toda方程和相对论Toda方程的参数化可积系统族.本文利用组合数学中引入的Schensted插入算法，导出了含有多种球的$ε$ -BBS，并给出了它的守恒量.为了证明这一点，我们扩展双有理变换的连续基本Toda轨道的离散饥饿的基本Toda轨道。
英文摘要：
The $ε$-BBS is the family of solitonic cellular automata obtained via the ultradiscretization of the elementary Toda orbits, which is a parametrized family of integrable systems unifying the Toda equation and the relativistic Toda equation. In this paper, we derive the $ε$-BBS with many kinds of balls and give its conserved quantities by the Schensted insertion algorithm which is introduced in combinatorics. To prove this, we extend birational transformations of the continuous elementary Toda orbits to the discrete hungry elementary Toda orbits.
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