Large sets of $t$-designs from groups

Rok, strany: 2009, 19 - 38

This paper addresses questions related to the existence and construction of \textit{large sets} of $t-(v,k,λ)$ designs. It contains material from my talk in the Combinatorial Designs Conference in honor of Alex Rosa's 70th birthday, which took place in beautiful Bratislava, in July, 2007. Naturally, only a small number of ``highlight'' topics could be included, and for the most part these involve the use of \textit{symmetry}, that is, it is assumed that the particular designs or large sets of designs, are invariant under a prescribed group of automorphisms. I present almost no proofs, but give references so that the reader can find a much wider repertory of theorems and constructions in the literature. For completeness, I include the statement of a few recursive constructions. The latter are extremely important on their own right, and deserve extensive attention elsewhere. I hope the reader becomes interested in the intriguing open problems posed at the end of the paper and succeeds in solving some of them.

ISO 690:

Magliveras, S. 2009. Large sets of $t$-designs from groups. In Mathematica Slovaca, vol. 59, no.1, pp. 19-38. 0139-9918. DOI: https://doi.org/10.2478/s12175-008-0109-9

APA:

Magliveras, S. (2009). Large sets of $t$-designs from groups. Mathematica Slovaca, 59(1), 19-38. 0139-9918. DOI: https://doi.org/10.2478/s12175-008-0109-9