A recreational puzzle posed 175 years ago of 15 schoolgirls to
walk three abreast to school for seven days of the week so that no girl
sees a friend repeated in her row has links to many areas of
mathematics: combinatorics, finite projective geometries, design and
coding theory, etc. There is an interesting historic link of this
problem to the 1938 Bombay Science Congress, resulting in a branch of
mathematics born in India. The problem can also be linked to states and
operators of two qubits in today's quantum information, those Lie
algebras and groups also providing a systematic way to get the required
arrangements of the girls. These patterns, that can be further linked to
four-colour vision and analogs in acoustics and sound, will be
discussed. They may be useful for manipulating states and operators of a
pair of qubits, with generalization also to multiple qubits.
Speaker's webpage: http://www.phys.lsu.edu/faculty/rau/