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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.14742 |
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| _version_ | 1866929380504109056 |
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| author | Elizarov, Nikita Grigoriev, Dima |
| author_facet | Elizarov, Nikita Grigoriev, Dima |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_14742 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A tropical version of Hilbert polynomial (in dimension one) Elizarov, Nikita Grigoriev, Dima Algebraic Geometry 14T05 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. |
| title | A tropical version of Hilbert polynomial (in dimension one) |
| topic | Algebraic Geometry 14T05 |
| url | https://arxiv.org/abs/2111.14742 |