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All directed BIBDs with k = 3 exist

Journal Article


Abstract


  • A directed BIBD with parameters (υ, b, r, k, λ∗) is a BIBD with parameters (υ, b, r, k, 2λ∗) in which each ordered pair of varieties occurs together in exactly λ∗ blocks. It is shown that λ∗υ(υ − 1) ≡ 0 (mod 3) is a necessary and sufficient condition for the existence of a directed (υ, b, r, k, λ∗) BIBD with k = 3. © 1980, All rights reserved.

Publication Date


  • 1980

Citation


  • All directed BIBDs with k = 3 exist (1980). Journal of Combinatorial Theory. Series A, 29(2), 244-248. doi:10.1016/0097-3165(80)90014-X

Scopus Eid


  • 2-s2.0-0001718738

Web Of Science Accession Number


Start Page


  • 244

End Page


  • 248

Volume


  • 29

Issue


  • 2

Abstract


  • A directed BIBD with parameters (υ, b, r, k, λ∗) is a BIBD with parameters (υ, b, r, k, 2λ∗) in which each ordered pair of varieties occurs together in exactly λ∗ blocks. It is shown that λ∗υ(υ − 1) ≡ 0 (mod 3) is a necessary and sufficient condition for the existence of a directed (υ, b, r, k, λ∗) BIBD with k = 3. © 1980, All rights reserved.

Publication Date


  • 1980

Citation


  • All directed BIBDs with k = 3 exist (1980). Journal of Combinatorial Theory. Series A, 29(2), 244-248. doi:10.1016/0097-3165(80)90014-X

Scopus Eid


  • 2-s2.0-0001718738

Web Of Science Accession Number


Start Page


  • 244

End Page


  • 248

Volume


  • 29

Issue


  • 2