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

doi:10.1007/BF02784058

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 journal › Article › peer-review

37 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 language	English (US)
Pages (from-to)	305-319
Number of pages	15
Journal	Israel Journal of Mathematics
Volume	83
Issue number	3
DOIs	https://doi.org/10.1007/BF02784058
State	Published - Oct 1993
Externally published	Yes

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Mathematics(all)

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title = "Hanani triple systems",

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}.",

author = "Vanstone, {S. A.} and Stinson, {D. R.} and Schellenberg, {P. J.} and A. Rosa and R. Rees and Colbourn, {C. J.} and Carter, {M. W.} and Carter, {J. E.}",

year = "1993",

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T1 - Hanani triple systems

AU - Vanstone, S. A.

AU - Stinson, D. R.

AU - Schellenberg, P. J.

AU - Rosa, A.

AU - Rees, R.

AU - Colbourn, C. J.

AU - Carter, M. W.

AU - Carter, J. E.

PY - 1993/10

Y1 - 1993/10

N2 - 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}.

AB - 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}.

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Hanani triple systems

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