Questions tagged [combinatorial-design]
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4 questions
3
votes
3
answers
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Sylvester's extension of Kirkman's schoolgirls problem
The "schoolgirls problem" posed and answered by Kirkman in 1850 is:
"Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them ...
- 2,072
23
votes
7
answers
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Output the Steiner system S(5,8,24)
Output 759 "rows", each of which consists of 8 distinct integers in the range 0,1,...,23, with the property that every set of 5 integers in the range 0,1,...,23 is contained in exactly one ...
- 2,072
5
votes
2
answers
366
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Generate a Kirkman triple system
Given a universe of \$v\$ elements, a Kirkman triple system is a set of \$(v-1)/2\$ classes each having \$v/3\$ blocks each having three elements, so that
every pair of elements appears in exactly ...
- 4,749
15
votes
4
answers
700
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Output a Steiner quadruple system
A Steiner quadruple system \$SQS(n)\$ is a collection of subsets (blocks) of size 4 of a set \$S\$ of size \$n\$ such that every subset of \$S\$ of size 3 is in exactly one block. It is easy to show ...
- 4,749