Graphs emerging from the solutions to the periodic discrete Toda equation over finite fields
Exactly Solvable and Integrable Systems
2019-06-19 v3 Mathematical Physics
math.MP
Abstract
The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing a equivalence class of cyclic permutations to the initial values. We proved that the graphs are bi-directional and that they are composed of several arrays of complete graphs connected at one of their vertices.
Keywords
Cite
@article{arxiv.1511.04509,
title = {Graphs emerging from the solutions to the periodic discrete Toda equation over finite fields},
author = {Masataka Kanki and Yuki Takahashi and Tetsuji Tokihiro},
journal= {arXiv preprint arXiv:1511.04509},
year = {2019}
}
Comments
20 pages, 5 figures, NOLTA Vol. E7-N, No.3, Jul. 2016