Tropical recurrent sequences

07/27/2018

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by   Dima Grigoriev, et al.

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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.