A tropical version of Hilbert polynomial (in dimension one)
Algebraic Geometry
2024-06-12 v4
Abstract
For a tropical univariate polynomial 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 . Also we establish sharp bounds on the tropical entropy.
Cite
@article{arxiv.2111.14742,
title = {A tropical version of Hilbert polynomial (in dimension one)},
author = {Nikita Elizarov and Dima Grigoriev},
journal= {arXiv preprint arXiv:2111.14742},
year = {2024}
}