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Non-existence of a certain projective plane
Published online by Cambridge University Press: 09 April 2009
Extract
The question whether any projective plane of order ten exists or not, is an unsolved problem that has attracted some interest (see, for instance, [2]). A method, by which a plane might have been discovered, was suggested to me by a theorem in [1]: ‘If order of a plane is greater than 10, a six-arc is not complete’. Elementary arguments do not, it appears, exclude the possibility of a complete six-arc in a plane of order ten: but they do show that such a figure would be of an extreme type, and that the whole plane would fit round it in a particular way. The limitation, in fact, is so severe that it becomes feasible to consider, for a good many of the incidences in the plane, all the alternative arrangements that seem possible. With the help of the Elliott 4130 computer of the University of Leicester, I have carried out an exhaustive search, and discovered that it is impossible to build up a projective plane by this method. So I can assert:
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 10 , Issue 1-2 , August 1969 , pp. 214 - 218
- Copyright
- Copyright © Australian Mathematical Society 1969
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