Naslov
Looking for additive Steiner 2-designs

Autori
Nakić, Anamari

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, kratko priopćenje, znanstveni

Izvornik
Combinatorics 2022 / - , 2022, 107-107

Skup
Combinatorics 2022

Mjesto i datum
Mantova, Italija, 30.05.2022. - 03.06.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Additive designs ; Steiner designs

Sažetak
A 2-(v, k, λ) design is additive under an abelian group G if, up to isomorphism, the point-set is a subset of G and each block sums to zero. What we found intriguing was that additive Steiner 2- designs appeared in short supply ; the only known classes were the point-line designs of AG(n, q) if q > 2, and of PG(n, q) if either n or q is 2. Also, the only known sporadic example was the famous 2-analog of a 2-(13, 3, 1) design found in [1] which is an additive 2-(8191, 7, 1) design. Thus all known Steiner 2-designs had block-size k equal to a prime power or a prime power plus one. Even though we proved their existence for any k not congruent to 2 (mod 4) not of the form 2 = n^3, it is disappointing that the values of v are huge. On the other hand we just found a pair of “small” additive Steiner 2-designs not lying in the above mentioned classes ; a 2-(40, 4, 1) design which is additive under Z_3^4 and a 2-(124, 4, 1) design which is additive under Z_5^3.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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