All Directed BIBDs with k = 3 Exist

نویسندگان

  • Jennifer Seberry
  • David B. Skillicorn
چکیده

A directed BIBD with parameters (v,b,r,k,λ*) is a BIBD with parameters (v, b, r, k, 2λ*) in which each ordered pair of varieties occurs together in exactly λ* blocks. It is shown that λ*v(v 1) = 0 (mod 3) is a necessary and sufficient condition for the existence of a directed (v, b, r, k, λ*) BIBD with k = 3. Disciplines Physical Sciences and Mathematics Publication Details Seberry, J and Skillicorn, D, All directed BIBDs with k = 3 exist, Journal of Combinatorial Theory, Ser. A, 29, 1980, 244-248. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/1000 Reprinted from JOURNAL OF CoMBINATORIAL THEORY, Series A An RiJ.lhco Reserved by Academic Press, New-York and London Note Vol. ~9, No.2, September 198(/ Prim.d'n B.igiu,,{ All Directed BIBDs with k = 3 Exist

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عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 29  شماره 

صفحات  -

تاریخ انتشار 1980