Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T11:44:06.014Z Has data issue: false hasContentIssue false
  • English
  • Français

Incidence matrices

Published online by Cambridge University Press:  26 February 2010

J. W. Archbold
J. W. Archbold
Affiliation:
University College, London, W.C.I.
Get access

Extract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Brack, R. H., “Difference sets in a finite group”, Trans. American Math. Soc., 78 (1955), 464–481.CrossRefGoogle Scholar
2.Chowla, S. and Ryser, H. J., “Combinatorial problems”, Canadian J. Maths., 2 (1950), 93–99.CrossRefGoogle Scholar
3.Hall, M. Jr., “Cyclic projective planes”, Duke Math. J., 14 (1947), 1079–1090.Google Scholar
4.König, D., Theorie der endlichen und unendlichen Graphen (New York, 1950), 170–178.Google Scholar
5.Frobenius, G., “Über zerlegbare Determinanten”, Sitzungesberichte der preussischen Akademie, 1 (1917), 274–277.Google Scholar
6.Mann, H. B. and Ryser, H. J., “Systems of distinct representatives”, American Math. Monthly, 60 (1953), 397–401.CrossRefGoogle Scholar