A Theorem on Steiner Systems
Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 1010-1015
Voir la notice de l'article provenant de la source Cambridge University Press
1. Definitions and notation. A generalized Steiner system (t-design, tactical configuration) with parameters t, λt, k, v is a system (T, B), where T is a set of v elements, B is a set of blocks each of which is a k-subset of T (but note that blocks bi and bj may be the same k-subset of T) and such that every set of t elements of T belongs to exactly λt of the blocks. If we put λt = u we denote by Su(t, k, v) the collection of all systems with these parameters. Thus Q ∈ Su(t, k, v) means Q = (T, B) is a system with the given parameters. If λt = u = 1, we write S(t, k, v) instead of S 1(t, k, v) and refer to the system as a Steiner system. If t = 2, the system is called a balanced incomplete block design.
Mendelsohn, N. S. A Theorem on Steiner Systems. Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 1010-1015. doi: 10.4153/CJM-1970-117-0
@article{10_4153_CJM_1970_117_0,
author = {Mendelsohn, N. S.},
title = {A {Theorem} on {Steiner} {Systems}},
journal = {Canadian journal of mathematics},
pages = {1010--1015},
year = {1970},
volume = {22},
number = {5},
doi = {10.4153/CJM-1970-117-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1970-117-0/}
}
[1] 1. Mendelsohn, N. S., Intersection numbers of t-designs, Notices Amer. Math. Soc. 16 (1969), 984. (Also University of Manitoba mimeographed series.) Google Scholar
[2] 2. Riordan, J., Combinatorial identities (Wiley, New York, 1968). Google Scholar
[3] 3. Witt, E., Ùber Steinersche Systems, Abh. Math. Sem. Hamburg Univ. 12 (1938), 265–275. Google Scholar
Cité par Sources :