## An automorphism group of a nontrivial (possibly infinite) Steiner triple system has at least as many block-orbits as point-orbits. The proof is a translation of that in the finite case, with a small twist. For block size 4, the argument fails, and, indeed, the stronger statement (involving blo
An orbit theorem for designs
β Scribed by Henry Beker
- Publisher
- Springer
- Year
- 1976
- Tongue
- English
- Weight
- 296 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0046-5755
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Dehon, M., An existence theorem for some simple t-designs, Discrete Mathematics 90 (1991) 137-142. ## Let S' be a simple S;(t, k, [) containing b' blocks and let S be a, not necessarily simple, $(t, 1. u); we prove that if b"(A -1) < (:), then there exists a simple &,(t, k, v). We apply this resu
The following result gives a partial answer to a question of R. M. Wilson regarding the existence of group divisible designs of large order. Let k and u be positive integers, 2 [ k [ u. Then there exists an integer m 0 =m 0 (k, u) such that there exists a group divisible design of group type m u wit
In this paper, we define the observer design problem for periodic orbits of nonlinear systems and solve the exponential observer design problem by geometric methods. First, we obtain necessary and sufficient conditions for local exponential observers for periodic orbits that are Lyapunov stable. We
We generalize some existence theorems for t- (u,k,l) designs. In fact, we prove that if certain inequality holds involving parameters of some simple r-designs, then new simple t-designs can be constructed. Using these results we discover first examples of infinite families of 5-designs in which blo