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Zero-sum flows in designs

Akbari, S ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1002/jcd.20289
  3. Publisher: 2011
  4. Abstract:
  5. Let D be a t-(v, k, λ) design and let N i(D), for 1≤i≤t, be the higher incidence matrix of D, a (0, 1)-matrix of size(v/i×b), where b is the number of blocks of D. A zero-sum flow of D is a nowhere-zero real vector in the null space of N1(D). A zero-sum k-flow of D is a zero-sum flow with values in {1,..., ±(k-1)}. In this article, we show that every non-symmetric design admits an integral zero-sum flow, and consequently we conjecture that every non-symmetric design admits a zero-sum 5-flow. Similarly, the definition of zero-sum flow can be extended to Ni(D), 1≤i≤t. Let D=t - (v.k,(v-t/k-t))be the complete design. We conjecture that Nt(D) admits a zero-sum 3-flow and prove this conjecture for t = 2
  6. Keywords:
  8. Source: Journal of Combinatorial Designs ; Volume 19, Issue 5 , 2011 , Pages 355-364 ; 10638539 (ISSN)
  9. URL: http://onlinelibrary.wiley.com/doi/10.1002/jcd.20289/abstract