Naslov
BIBD's for (13, 5, 5), (16, 6, 5) and (21, 6, 4) Possessing Possibly an Automorphism of Order 3

Autori
Martinjak, Ivica ; Pavčević, Mario-Osvin

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
World Academy of Science, Engineering and Technology Volume 58 / Cemal Ardil - Venecija : World Academy of Science, Engineering and Technology (WASET), 2009, 885-888

Skup
International Conference on Computer and Applied Mathematics

Mjesto i datum
Venecija, Italija, 28.10.2009. - 30.10.2009

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
BIBD; incidence matrix; automorphism group; tactical decomposition; deterministic algorithm

Sažetak
When trying to enumerate all BIBD's for given parameters, their natural solution space appears to be huge and grows extremely with the number of points of the design. Therefore, constructive enumerations are often carried out by assuming additional constraints on design's structure, automorphisms being mostly used ones. It remains a hard task to construct designs with trivial automorphism groups - those with no additional symmetry - although it is believed that the most of the BIBD's belong to that case. In this paper, very many new designs with parameters 2-(13, 5, 5), 2-(16, 6, 5) and 2-(21, 6, 4) are constructed, assuming an action of an automorphism of order 3. Even more, it was possible to construct millions of such designs with no non-trivial automorphisms.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA