On Freiman's Theorem in a function field setting
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913353968910336 |
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| author | Wessel, Mieke |
| author_facet | Wessel, Mieke |
| contents | We prove some new instances of a conjecture of Bachoc, Couvreur and Zémor that generalizes Freiman's $3k-4$ Theorem to a multiplicative version in a function field setting. As a consequence we find that if $F$ is a rational function field over an algebraically closed field $K$ and $S \subset F$ a finite dimensional $K$-vector space such that $\dim S^2 = 2\dim S + 1$, then the conjecture holds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Freiman's Theorem in a function field setting Wessel, Mieke Number Theory Combinatorics We prove some new instances of a conjecture of Bachoc, Couvreur and Zémor that generalizes Freiman's $3k-4$ Theorem to a multiplicative version in a function field setting. As a consequence we find that if $F$ is a rational function field over an algebraically closed field $K$ and $S \subset F$ a finite dimensional $K$-vector space such that $\dim S^2 = 2\dim S + 1$, then the conjecture holds. |
| title | On Freiman's Theorem in a function field setting |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2405.10724 |