2021/11/29 by Nikita Elizarov, Elizarov, Nikita, Dima Grigoriev +1
Computer Science · Mathematics · #14T05 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2111.14742
openalex publication_date 2021/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.