A Classification of the flag-transitive $2$-$(v,k,2)$ designs
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914739229032448 |
|---|---|
| author | Liang, Hongxue Montinaro, Alessandro |
| author_facet | Liang, Hongxue Montinaro, Alessandro |
| contents | In this paper, we provide a complete classification of $2$-$(v,k,2)$ design admitting a flag-transitive automorphism group of affine type with the only exception of the semilinear $1$-dimensional group. Alongside this analysis we provide a construction of seven new families of such flag-transitive $2$-designs, two of them infinite, and some of them involve remarkable objects such as $t$-spreads, translation planes, quadrics and Segre varieties.
Our result together with those Alavi et al. [1,2], Praeger et al. [15], Zhou and the first author [37,38] provides a complete classification of $2$-$(v,k,2)$ design admitting a flag-transitive automorphism group with the only exception of the semilinear $1$-dimensional case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02311 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Classification of the flag-transitive $2$-$(v,k,2)$ designs Liang, Hongxue Montinaro, Alessandro Combinatorics Group Theory 05B05, 05B25, 20B25 In this paper, we provide a complete classification of $2$-$(v,k,2)$ design admitting a flag-transitive automorphism group of affine type with the only exception of the semilinear $1$-dimensional group. Alongside this analysis we provide a construction of seven new families of such flag-transitive $2$-designs, two of them infinite, and some of them involve remarkable objects such as $t$-spreads, translation planes, quadrics and Segre varieties. Our result together with those Alavi et al. [1,2], Praeger et al. [15], Zhou and the first author [37,38] provides a complete classification of $2$-$(v,k,2)$ design admitting a flag-transitive automorphism group with the only exception of the semilinear $1$-dimensional case. |
| title | A Classification of the flag-transitive $2$-$(v,k,2)$ designs |
| topic | Combinatorics Group Theory 05B05, 05B25, 20B25 |
| url | https://arxiv.org/abs/2404.02311 |