Kirkman's Schoolgirls Wearing Hats and Walking through Fields of Numbers
The Kirkman schoolgirls problem, a famous gem due to T. P. Kirkman in the mid 19th century, asks for 7 distinct arrangements of 15 girls into 5 rows of 3 girls each with the condition that each girl walks in a row with every other girl exactly once. Solutions to this famous problem can be found in algebraic number fields, finite projective 3-space, and certain error-correcting codes. These connections are made in the present article, along with a thorough explanation of the underlying mathematical objects. Related questions are posed and surprising connections are realized.
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Document Type: Research Article
Publication date: 2009-02-01
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