Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Algebraic Geometry

arXiv:1807.10714 (math)
[Submitted on 27 Jul 2018 (v1), last revised 4 Feb 2020 (this version, v5)]

Title:Tropical recurrent sequences

Authors:Dima Grigoriev
View PDF
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.
Comments: it is described when the entropy is positive
Subjects: Algebraic Geometry (math.AG); Symbolic Computation (cs.SC)
MSC classes: 14T05
Cite as: arXiv:1807.10714 [math.AG]
  (or arXiv:1807.10714v5 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.10714

Submission history

From: Dima Grigoriev [view email]
[v1] Fri, 27 Jul 2018 16:34:16 UTC (10 KB)
[v2] Tue, 4 Sep 2018 16:27:23 UTC (12 KB)
[v3] Wed, 7 Nov 2018 17:14:38 UTC (15 KB)
[v4] Fri, 22 Mar 2019 13:47:17 UTC (15 KB)
[v5] Tue, 4 Feb 2020 20:15:38 UTC (20 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.AG
< prev   |   next >
new | recent | 2018-07
Change to browse by:
cs
cs.SC
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)