Transitive $(q-1)$-fold packings of $\rm{PG}_n(q)$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910314678714368 |
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| author | Hawtin, Daniel R. |
| author_facet | Hawtin, Daniel R. |
| contents | A $t$-fold packing of a projective space $\rm{PG}_n(q)$ is a collection $\mathcal{P}$ of line-spreads such that each line of $\rm{PG}_n(q)$ occurs in precisely $t$ spreads in $\mathcal{P}$. A $t$-fold packing $\mathcal{P}$ is transitive if a subgroup of $\rm{PΓL}_{n+1}(q)$ preserves and acts transitively on $\mathcal{P}$. We give a construction for a transitive $(q-1)$-fold packing of $\rm{PG}_n(q)$, where $q=2^k$, for any odd positive integers $n$ and $k$, such that $n\geq 3$. This generalises a construction of Baker from 1976 for the case $q=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transitive $(q-1)$-fold packings of $\rm{PG}_n(q)$ Hawtin, Daniel R. Combinatorics 05B25 (Primary) 05B40, 52C17 (Secondary) A $t$-fold packing of a projective space $\rm{PG}_n(q)$ is a collection $\mathcal{P}$ of line-spreads such that each line of $\rm{PG}_n(q)$ occurs in precisely $t$ spreads in $\mathcal{P}$. A $t$-fold packing $\mathcal{P}$ is transitive if a subgroup of $\rm{PΓL}_{n+1}(q)$ preserves and acts transitively on $\mathcal{P}$. We give a construction for a transitive $(q-1)$-fold packing of $\rm{PG}_n(q)$, where $q=2^k$, for any odd positive integers $n$ and $k$, such that $n\geq 3$. This generalises a construction of Baker from 1976 for the case $q=2$. |
| title | Transitive $(q-1)$-fold packings of $\rm{PG}_n(q)$ |
| topic | Combinatorics 05B25 (Primary) 05B40, 52C17 (Secondary) |
| url | https://arxiv.org/abs/2402.00780 |