On subspaces defining linear sets of maximum rank
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917897358540800 |
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| author | Pepe, Valentina |
| author_facet | Pepe, Valentina |
| contents | Let $V$ denote an $r$-dimensional $\mathbb{F}_{q^n}$-vector space. Let $U$ and $W$ be $\mathbb{F}_q$-subspaces of $V$, $L_U$ and $L_W$ the projective points of $\mathrm{PG}\,(V,q^n)$ defined by $U$ and $W$ respectively. We address the problem when $L_W=L_U$ under the hypothesis that $U$ and $W$ have maximum dimension, i.e., $\dim_{\mathbb{F}_q} W=\dim_{\mathbb{F}_q}U=$ $rn-n $, and we give a complete characterization for $r=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01551 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On subspaces defining linear sets of maximum rank Pepe, Valentina Combinatorics 51A05, 14M15, 12E20 Let $V$ denote an $r$-dimensional $\mathbb{F}_{q^n}$-vector space. Let $U$ and $W$ be $\mathbb{F}_q$-subspaces of $V$, $L_U$ and $L_W$ the projective points of $\mathrm{PG}\,(V,q^n)$ defined by $U$ and $W$ respectively. We address the problem when $L_W=L_U$ under the hypothesis that $U$ and $W$ have maximum dimension, i.e., $\dim_{\mathbb{F}_q} W=\dim_{\mathbb{F}_q}U=$ $rn-n $, and we give a complete characterization for $r=2$. |
| title | On subspaces defining linear sets of maximum rank |
| topic | Combinatorics 51A05, 14M15, 12E20 |
| url | https://arxiv.org/abs/2403.01551 |