Computing of the dimensions of the components of tropical prevarieties described by linear tropical recurrent relations
Abstract
The main goal of this paper is the study of tropical recurrent sequences determined by various relations. Tropical mathematics is a recent field of modern mathematics. It has many applications in algebra, geometry, computer science, biology, economics and engineering. At the same time, many topical issues of tropical mathematics are not sufficiently studied up to now. For a set of tropical recurrent sequences described by tropical relations, D. Grigoriev put forward a hypothesis of stabilization of the maximum dimensions of the components of tropical prevarieties. This hypothesis has not yet been proven. As a part of this work, for various linear tropical recurrent sequences, the appropriate tropical prevarieties were examined using the gfan package in order to check Grigoriev’s hypothesis. The validity of such a hypothesis would make it possible to calculate the corresponding dimension for a recurrent sequence for an arbitrary length.
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