Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.14742 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
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.