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Incidence matrices

Published online by Cambridge University Press:  26 February 2010

J. W. Archbold
J. W. Archbold
Affiliation:
University College, London, W.C.I.
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The incidence matrices for the finite projective planes, for the so-called λ-planes (where two lines meet in λ points instead of the usual 1) and for some other configurations, including those of Pappus and Desargues, are all cases of what are defined below as (v, k, t, λ)-matrices. These are shown here to possess arithmetical properties which reduce, in the case of cyclic projective planes, to properties remarked on by Marshall Hall [3]. And if a certain group hypothesis (which suggests itself in a natural way) is satisfied by a matrix of this type, the matrix is shown to be equivalent (by rearranging the rows and columns) to a direct sum of incidence matrices for λ-planes, each of which satisfies the same group hypothesis.

Type
Research Article
Information
Mathematika , Volume 7 , Issue 1 , June 1960 , pp. 41 - 49
Copyright
Copyright © University College London 1960

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References

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