The fine structure of threefold triple systems: υ ≡ 1 or 3 (mod 6)

Charles J. Colbourn; Rudolf A. Mathon; Alexander Rosa; Nabil Shalaby

doi:10.1016/0012-365X(91)90266-5

The fine structure of threefold triple systems: υ ≡ 1 or 3 (mod 6)

Charles J. Colbourn
, Rudolf A. Mathon
, Alexander Rosa
, Nabil Shalaby

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

The fine structure of a triple system of index λ is the vector (c₁, ..., c_λ), where c₁ is the number of triples appearing precisely i times in the system. We determine necessary conditions for a vector to be the fine structure of a threefold triple system and prove the sufficiency of these conditions for all υ ≡ 1, 3 (mod 6), υ ≥ 19.

Original language	English (US)
Pages (from-to)	49-64
Number of pages	16
Journal	Discrete Mathematics
Volume	92
Issue number	1-3
DOIs	https://doi.org/10.1016/0012-365X(91)90266-5
State	Published - Nov 17 1991
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(91)90266-5

Cite this

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abstract = "The fine structure of a triple system of index λ is the vector (c1, ..., cλ), where c1 is the number of triples appearing precisely i times in the system. We determine necessary conditions for a vector to be the fine structure of a threefold triple system and prove the sufficiency of these conditions for all υ ≡ 1, 3 (mod 6), υ ≥ 19.",

author = "Colbourn, \{Charles J.\} and Mathon, \{Rudolf A.\} and Alexander Rosa and Nabil Shalaby",

note = "Funding Information: of the authors is supported by NSERC",

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AU - Rosa, Alexander

AU - Shalaby, Nabil

N1 - Funding Information: of the authors is supported by NSERC

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AB - The fine structure of a triple system of index λ is the vector (c1, ..., cλ), where c1 is the number of triples appearing precisely i times in the system. We determine necessary conditions for a vector to be the fine structure of a threefold triple system and prove the sufficiency of these conditions for all υ ≡ 1, 3 (mod 6), υ ≥ 19.

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JO - Discrete Mathematics

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The fine structure of threefold triple systems: υ ≡ 1 or 3 (mod 6)

Abstract

ASJC Scopus subject areas

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