Constructions for cyclic Steiner 2-designs. (English) Zbl 0647.05015
Combinatorial design theory, Dedic. A. Rosa Occas. 50th Birthday, Ann. Discrete Math. 34, 353-362 (1987).
[For the entire collection see Zbl 0625.00011.]
This paper surveys direct and recursive constructions for cyclic Steiner 2-designs (cyclic BIBD’s with \(\lambda =1)\). A new method is presented for cyclic designs with blocks having a prime number of elements. Several new constructions are given for block sizes 4 and 5 which extend earlier existence results. Some of these new constructions are based on perfect difference families and on additive sequences of permutations. The paper concludes with a list of open problems.
This paper surveys direct and recursive constructions for cyclic Steiner 2-designs (cyclic BIBD’s with \(\lambda =1)\). A new method is presented for cyclic designs with blocks having a prime number of elements. Several new constructions are given for block sizes 4 and 5 which extend earlier existence results. Some of these new constructions are based on perfect difference families and on additive sequences of permutations. The paper concludes with a list of open problems.
Reviewer: J.Dinitz
MSC:
| 05B10 | Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) |
| 05B05 | Combinatorial aspects of block designs |
