| Title:
|
Some Additive $2-(v, 5,\lambda )$ Designs (English) |
| Author:
|
Caggegi, Andrea |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
65-80 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Given a finite additive abelian group $G$ and an integer $k$, with $3\le k \le |G|$, denote by $\mathcal {D}_k (G)$ the simple incidence structure whose point-set is $G$ and whose blocks are the $k$-subsets $C = \lbrace c_1, c_2,\dots , c_k\rbrace $ of $G$ such that $c_1 + c_2+\dots +c_k = 0$. It is known (see [Caggegi, A., Di Bartolo, A., Falcone, G.: Boolean 2-designs and the embedding of a 2-design in a group arxiv 0806.3433v2, (2008), 1–8.]) that $\mathcal {D}_k (G)$ is a 2-design, if $G$ is an elementary abelian $p$-group with $p$ a prime divisor of $k$. From [Caggegi, A., Falcone, G., Pavone, M.: On the additivity of block design submitted.] we know that $\mathcal {D}_3(G)$ is a 2-design if and only if $G$ is an elementary abelian 3-group. It is also known (see [Caggegi, A.: Some additive $2-(v,4,\lambda )$ designs Boll. Mat. Pura e Appl. 2 (2009), 1–3.]) that $G$ is necessarily an elementary abelian 2-group, if $\mathcal {D}_4(G)$ is a 2-design. Here we shall prove that $\mathcal {D}_5(G)$ is a 2-design if and only if $G$ is an elementary abelian 5-group. (English) |
| Keyword:
|
Conformal mapping |
| Keyword:
|
geodesic mapping |
| Keyword:
|
conformal-geodesic mapping |
| Keyword:
|
initial conditions |
| Keyword:
|
(pseudo-) Riemannian space |
| MSC:
|
53B20 |
| MSC:
|
53B30 |
| MSC:
|
53C21 |
| idZBL:
|
Zbl 1344.05026 |
| idMR:
|
MR3468601 |
| . |
| Date available:
|
2015-09-01T08:59:35Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144368 |
| . |
| Reference:
|
[1] Beth, T., Jungnickel, D., Lenz, H.: Design Theory. 2nd ed., Cambridge University Press, Cambridge, 1999. Zbl 0945.05005, MR 0890103 |
| Reference:
|
[2] Caggegi, A., Di Bartolo, A., Falcone, G.: Boolean 2-designs and the embedding of a 2-design in a group. arxiv 0806.3433v2, (2008), 1–8. MR 3468601 |
| Reference:
|
[3] Caggegi, A., Falcone, G., Pavone, M.: On the additivity of block design. submitted. |
| Reference:
|
[4] Caggegi, A.: Some additive $2-(v,4,\lambda )$ designs. Boll. Mat. Pura e Appl. 2 (2009), 1–3. Zbl 1255.05028 |
| Reference:
|
[5] Colbourn, C. J., Dinitz, J. H.: The CRC Handbook of Combinatorial Designs. Discrete Mathematics and Its Applications, 2nd ed., Chapman & Hall/CRC Press, 2007. Zbl 1101.05001, MR 2246267 |
| . |
