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Bibliographic Details
Main Authors: Elizarov, Nikita, Grigoriev, Dima
Format: Preprint
Published: 2021
Subjects:
Online Access:https://arxiv.org/abs/2111.14742
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Table of Contents:
  • For a tropical univariate polynomial $f$ we define its tropical Hilbert function as the dimension of a tropical linear prevariety of solutions of the tropical Macauley matrix of the polynomial up to a (growing) degree. We show that the tropical Hilbert function equals (for sufficiently large degrees) a sum of a linear function and a periodic function with an integer period. The leading coefficient of the linear function coincides with the tropical entropy of $f$. Also we establish sharp bounds on the tropical entropy.