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Dimension of the space generated by Steiner systems.
- Source :
- Journal of Combinatorial Designs; May2019, Vol. 27 Issue 5, p295-310, 16p
- Publication Year :
- 2019
-
Abstract
- To every Steiner system with parameters (t,k,v) on {1,...,v} and blocks B, we can assign its characteristic vector χB, which is a (0,1)‐vector whose entries are indexed by the k‐subsets of {1,...,v} such that for each k‐subset A of {1,...,v},χB(A)=1 if and only if A∈B. In this paper, we show that the dimension of the vector space generated by all of the characteristic vectors of Steiner systems with parameters (t,k,v) is (vk)−(vt)+1, provided that 1≤t≤k≤v/2 and there is at least one such system. [ABSTRACT FROM AUTHOR]
- Subjects :
- STEINER systems
VECTOR spaces
SET theory
BLOCK designs
DIMENSION theory (Algebra)
Subjects
Details
- Language :
- English
- ISSN :
- 10638539
- Volume :
- 27
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Journal of Combinatorial Designs
- Publication Type :
- Academic Journal
- Accession number :
- 135059541
- Full Text :
- https://doi.org/10.1002/jcd.21649