The spectrum of support sizes for threefold triple systems

Charles J. Colbourn; Ebadollah S. Mahmoodian

doi:10.1016/0012-365X(90)90216-5

The spectrum of support sizes for threefold triple systems

Charles J. Colbourn, Ebadollah S. Mahmoodian

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12 Scopus citations

Abstract

The spectrum of possible numbers of distinct blocks in a threefold triple system of order v is determined. Let m_υ = ⌊ υ(υ-1) 6⌋. A threefold triple system with υ ≡ 1, 3 (mod 6) elements can have any number of distinct blocks from, and only from, {m_υ,m_υ + 4, m_υ + 6, m_υ + 7,⋯, 3m_υ} provided υ≠3, 7, 9. A threefold triple system with υ≡5 (mod 6) elements can have any number of distinct blocks from, and only from, {m_υ + 7, m_υ + 10, m_υ + 11,⋯, 3m_υ + 1}.

Original language	English (US)
Pages (from-to)	9-19
Number of pages	11
Journal	Discrete Mathematics
Volume	83
Issue number	1
DOIs	https://doi.org/10.1016/0012-365X(90)90216-5
State	Published - Jul 1 1990
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(90)90216-5

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abstract = "The spectrum of possible numbers of distinct blocks in a threefold triple system of order v is determined. Let mυ = ⌊ υ(υ-1) 6⌋. A threefold triple system with υ ≡ 1, 3 (mod 6) elements can have any number of distinct blocks from, and only from, {mυ,mυ + 4, mυ + 6, mυ + 7,⋯, 3mυ} provided υ≠3, 7, 9. A threefold triple system with υ≡5 (mod 6) elements can have any number of distinct blocks from, and only from, {mυ + 7, mυ + 10, mυ + 11,⋯, 3mυ + 1}.",

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AU - Mahmoodian, Ebadollah S.

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N2 - The spectrum of possible numbers of distinct blocks in a threefold triple system of order v is determined. Let mυ = ⌊ υ(υ-1) 6⌋. A threefold triple system with υ ≡ 1, 3 (mod 6) elements can have any number of distinct blocks from, and only from, {mυ,mυ + 4, mυ + 6, mυ + 7,⋯, 3mυ} provided υ≠3, 7, 9. A threefold triple system with υ≡5 (mod 6) elements can have any number of distinct blocks from, and only from, {mυ + 7, mυ + 10, mυ + 11,⋯, 3mυ + 1}.

AB - The spectrum of possible numbers of distinct blocks in a threefold triple system of order v is determined. Let mυ = ⌊ υ(υ-1) 6⌋. A threefold triple system with υ ≡ 1, 3 (mod 6) elements can have any number of distinct blocks from, and only from, {mυ,mυ + 4, mυ + 6, mυ + 7,⋯, 3mυ} provided υ≠3, 7, 9. A threefold triple system with υ≡5 (mod 6) elements can have any number of distinct blocks from, and only from, {mυ + 7, mυ + 10, mυ + 11,⋯, 3mυ + 1}.

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The spectrum of support sizes for threefold triple systems

Abstract

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