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

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Algebraic Combinatorics Pub Date : 2024-07-01 DOI:10.1007/s10801-024-01338-7

Katsuki Kobayashi, Satoshi Tsujimoto

引用次数: 0

Abstract

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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$$epsilon$$-BBS和申斯泰德插入算法的一般化

(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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebraic Combinatorics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Algebraic Combinatorics provides a single forum for papers on algebraic combinatorics which, at present, are distributed throughout a number of journals. Within the last decade or so, algebraic combinatorics has evolved into a mature, established and identifiable area of mathematics. Research contributions in the field are increasingly seen to have substantial links with other areas of mathematics. The journal publishes papers in which combinatorics and algebra interact in a significant and interesting fashion. This interaction might occur through the study of combinatorial structures using algebraic methods, or the application of combinatorial methods to algebraic problems.