Loading...

Dimension of the space generated by Steiner systems

Ghodrati, A. H ; Sharif University of Technology | 2019

161 Viewed
  1. Type of Document: Article
  2. DOI: 10.1002/jcd.21649
  3. Publisher: John Wiley and Sons Inc , 2019
  4. Abstract:
  5. To every Steiner system with parameters (t, k, v) on {1,…, v} and blocks B, we can assign its characteristic vector X 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}, X 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 (Formula presented.), provided that 1 ≤ t ≤ k ≤ v/2 and there is at least one such system. © 2019 Wiley Periodicals, Inc
  6. Keywords:
  7. Steiner systems ; Vectors ; Characteristic vectors ; Steiner systems ; Vector spaces
  8. Source: Journal of Combinatorial Designs ; Volume 27, Issue 5 , 2019 , Pages 295-310 ; 10638539 (ISSN)
  9. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/jcd.21649