$$epsilon$$-BBS和申斯泰德插入算法的一般化

Pub Date : 2024-07-01 DOI:10.1007/s10801-024-01338-7

Katsuki Kobayashi, Satoshi Tsujimoto

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引用次数: 0

摘要

(epsilon)-BBS是通过对基本托达轨道进行超具体化而得到的独元胞自动机族，它是统一了托达方程和相对论托达方程的参数化可积分系统族。在本文中，我们推导了具有多种球的（\epsilon \）-BBS，并通过组合学中引入的申斯泰德插入算法给出了它的守恒量。为了证明这一点，我们将连续初等户田轨道的双向变换扩展到离散饿初等户田轨道。

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Generalization of the $$\epsilon $$ -BBS and the Schensted insertion algorithm

The $\epsilon $-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 $\epsilon $-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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