Dimension of the space generated by Steiner systems. Issue 5 (21st January 2019)

• Record Type: Journal Article
• Authors: Ghodrati, Amir Hossein
• Is Part Of: Journal of combinatorial designs. Volume 27:Issue 5(2019:May)
• Page Start: 295
• Page End: 310
• Publication Date: 2019-01-21
• Subjects: Steiner systems; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21649
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: To every Steiner system with parameters ( t, k, v ) on { 1, …, v } and blocks B, we can assign its characteristic vector χ B, 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 }, χ B ( 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 ( v k ) − ( v t ) + 1, provided that 1 ≤ t ≤ k ≤ v / 2 and there is at least one such system.