Infinite families of strictly cyclic Steiner quadruple systems
β Scribed by Helmut Siemon
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 557 KB
- Volume
- 77
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
For definitions and preliminary results see also Section 2.
' See Section 3.1.
' For the convenience of the reader we repeat here the argument of the proof of Theorem 1 in with 2p a instead of 2 5".
π SIMILAR VOLUMES
Siemon, H., On the existence of cyclic Steiner Quadruple Systems SQS(2p), Discrete Mathematics 97 (1991) 377-385. Subsequent to Kohler's result in [l], Satz 8, we show that strictly cyclic SQS(2p), p prime number and p = 53, 77 ( 120) exist if a certain number theoretic claim can be proved. We verif
This paper gives some recursive constructions for cyclic 3-designs. Using these constructions we improve Grannell and Griggs's construction for cyclic Steiner quadruple systems, and many known recursive constructions for cyclic Steiner quadruple systems are unified. Finally, some new infinite famili
In this article, we construct overlarge sets of disjoint S(3, 4, 3 n -1) and overlarge sets of disjoint S(3, 4, 3 n + 1) for all n β₯ 2. Up to now, the only known infinite sequence of overlarge sets of disjoint S(3, 4, v) were the overlarge sets of disjoint S(3, 4, 2 n ) obtained from the oval conics
## Abstract A __Steiner quadruple system__ of order __v__ (briefly SQS (__v__)) is a pair (__X__, $\cal B$), where __X__ is a __v__βelement set and $\cal B$ is a set of 4βelement subsets of __X__ (called __blocks__ or __quadruples__), such that each 3βelement subset of __X__ is contained in a uniqu