Tropical recurrent sequences
Abstract
Tropical recurrent sequences are introduced satisfying a given vector (being a tropical counterpart of classical linear recurrent sequences). We consider the case when Newton polygon of the vector has a single (bounded) edge. In this case there are periodic tropical recurrent sequences which are similar to classical linear recurrent sequences. A question is studied when there exists a non-periodic tropical recurrent sequence satisfying a given vector, and partial answers are provided to this question. Also an algorithm is designed which tests existence of non-periodic tropical recurrent sequences satisfying a given vector with integer coordinates. Finally, we introduce a tropical entropy of a vector and provide some bounds on it.
Cite
@article{arxiv.1807.10714,
title = {Tropical recurrent sequences},
author = {Dima Grigoriev},
journal= {arXiv preprint arXiv:1807.10714},
year = {2020}
}
Comments
it is described when the entropy is positive