The spectrum for 2-perfect 6-cycle systems (Q1176380)
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scientific article; zbMATH DE number 14079
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The spectrum for 2-perfect 6-cycle systems |
scientific article; zbMATH DE number 14079 |
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The spectrum for 2-perfect 6-cycle systems (English)
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25 June 1992
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A 6-cycle system of order \(v\) is a partition of all unordered pairs on \(v\) points into hexagons; such a partition is 2-perfect if every unordered pair also occurs at distance two in exactly one of the hexagons. The distance two partition so induced is a Steiner triple system. The existence of 2-perfect 6-cycle systems is settled completely: one exists if and only if \(v\equiv 1,9\pmod{12}\) and \(v\neq 9\).
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spectrum
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cycle systems
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partition
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Steiner triple system
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