Hanani triple systems

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

Research output: Contribution to journalArticle

33 Citations (Scopus)

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

Fingerprint

Triple System
Pairwise
Disjoint
Steiner Triple System
Analogue
Partial
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Vanstone, S. A., Stinson, D. R., Schellenberg, P. J., Rosa, A., Rees, R., Colbourn, C., ... Carter, J. E. (1993). Hanani triple systems. Israel Journal of Mathematics, 83(3), 305-319. https://doi.org/10.1007/BF02784058

Hanani triple systems. / Vanstone, S. A.; Stinson, D. R.; Schellenberg, P. J.; Rosa, A.; Rees, R.; Colbourn, Charles; Carter, M. W.; Carter, J. E.

In: Israel Journal of Mathematics, Vol. 83, No. 3, 10.1993, p. 305-319.

Research output: Contribution to journalArticle

Vanstone, SA, Stinson, DR, Schellenberg, PJ, Rosa, A, Rees, R, Colbourn, C, Carter, MW & Carter, JE 1993, 'Hanani triple systems', Israel Journal of Mathematics, vol. 83, no. 3, pp. 305-319. https://doi.org/10.1007/BF02784058
Vanstone SA, Stinson DR, Schellenberg PJ, Rosa A, Rees R, Colbourn C et al. Hanani triple systems. Israel Journal of Mathematics. 1993 Oct;83(3):305-319. https://doi.org/10.1007/BF02784058
Vanstone, S. A. ; Stinson, D. R. ; Schellenberg, P. J. ; Rosa, A. ; Rees, R. ; Colbourn, Charles ; Carter, M. W. ; Carter, J. E. / Hanani triple systems. In: Israel Journal of Mathematics. 1993 ; Vol. 83, No. 3. pp. 305-319.
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