Hanani triple systems

S. A. Vanstone, D. R. Stinson, P. J. Schellenberg, A. Rosa, R. Rees, C. J. Colbourn, M. W. Carter, J. E. Carter

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

Hanani triple systems on v≡1 (mod 6) elements are Steiner triple systems having (v-1)/2 pairwise disjoint almost parallel classes (sets of pairwise disjoint triples that span v-1 elements), and the remaining triples form a partial parallel class. Hanani triple systems are one natural analogue of the Kirkman triple systems on v≡3 (mod 6) elements, which form the solution of the celebrated Kirkman schoolgirl problem. We prove that a Hanani triple system exists for all v≡1 (mod 6) except for v ∈ {7, 13}.

Original languageEnglish (US)
Pages (from-to)305-319
Number of pages15
JournalIsrael Journal of Mathematics
Volume83
Issue number3
DOIs
StatePublished - Oct 1993
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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