A completion conjecture for Kirkman triple systems (Q2785716)
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scientific article; zbMATH DE number 981891
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A completion conjecture for Kirkman triple systems |
scientific article; zbMATH DE number 981891 |
Statements
21 April 1997
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Kirkman triple system
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A completion conjecture for Kirkman triple systems (English)
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The conjecture is made that given any two parallel classes of triples on \(6t+3\) points which share no pair, there is a Kirkman triple system on \(6t+3\) points in which the two specified parallel classes form two of the \(3t+1\) classes in the resolution. The truth of the conjecture is immediate for 3 and 9 points, and easily checked for 15 points. The authors establish the conjecture for 21 points, and examine type uniform Kirkman triple systems in which the unions of any two distinct parallel classes are isomorphic.
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