Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T20:07:31.312Z Has data issue: false hasContentIssue false
  • English
  • Français

The Chords of the Non-Ruled Quadric In PG(3, 3)

Published online by Cambridge University Press:  20 November 2018

H. S. M. Coxeter
H. S. M. Coxeter*
Affiliation:
University of Toronto
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the preceding paper, Tutte described the forty-five chords of an “ellipsoid” in the finite space PG(3, 3), showing that they may be regarded as the edges of a remarkable graph whose group is the group of automorphisms of the symmetric group . The object of this sequel is to relate Tutte's idea to Sylvester's combinatorial investigation of the fifteen “duads” and fifteen “synthemes” formed by six symbols, and to Richmond's discussion of the figure of six points in a projective 4-space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 484 - 488
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Baker, H. F., Principles of geometry, vol. 2 (Cambridge, 1930).Google Scholar
2. Baker, H. F., Principles of geometry, vol. 4 (Cambridge, 1940).Google Scholar
3. Coxeter, H. S. M., Self-dual configurations and regular graphs, Bull. Amer. Math. Soc, 56 (1950), 413–455.Google Scholar
4.Edge, W. L., Geometry in three dimensions over GF(3),Proc. Royal Soc, A 222 (1954), 262-286.Google Scholar
5. Richmond, H. W., On the figure of six points in space of four dimensions, Quart. J. Math., 31 (1900), 125–160.Google Scholar
6. Sylvester, J . J ., Elementary researches in the analysis of combinatorial aggregation, Collected Mathematical Papers, vol. 1 (Cambridge, 1904).Google Scholar
7.Tutte, W. T., The chords of the non-ruled quadric in PG(3, 3), Can. J. Math., 10 (1958), 481-483.Google Scholar