Ordinary graphs and subplane partitions

@article{Fossorier2004OrdinaryGA,
  title={Ordinary graphs and subplane partitions},
  author={Marc P. C. Fossorier and Jaroslav Jezek and James B. Nation and Alex Pogel},
  journal={Discrete Mathematics},
  year={2004},
  volume={282},
  pages={137-148}
}
We introduce a generalization of symmetric (v, k, λ) block designs, and show how these could potentially be used to construct projective planes of non-prime-power order. If q is a prime power and n2 +n+1 = N(q2 +q+1), then conceivably we could construct a projective plane of order n by gluing together N planes of order q. For example, 182 +18+1 = 343 = 49 ·7. Can we make a projective plane of order 18 by gluing 49 planes of order 2? With this in mind, we will discuss a class of directed graphs… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.
2 Citations
12 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-2 of 2 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 12 references

Quadratic extensions of cyclic planes

  • R. H. Bruck
  • Proc. Symp. Appl. Math.,
  • 1960
Highly Influential
3 Excerpts

Proof of the prime power conjecture for projective planes of order n with abelian collineation groups of order n 2

  • D. Jungnickel A. Blokhuis, B. Schmidt
  • Proc . Amer . Math . Soc .
  • 2002

Ordinary graphs with a = 0 , manuscript , 2002 . [ 11 ] U . Ott , Endliche zyklische Ebenen

  • D. Stinson
  • Difference Sets , in : Contemporary Design Theory…
  • 1992

On a projective plane of order 11 with Frobenius group of order 21 ,

  • E. Kramer K. Horvatić-Baldasar, I. Matulić-Bedenić
  • Rad . Mat .
  • 1990

Characterization of projective planes of small prime orders

  • C. Y. Ho
  • J . Combin . Theory Ser . A
  • 1986

A subplane partition of the cyclic plane

  • Peter Yff
  • Arab J. Math
  • 1980

On orthogonal matrices

  • R. E. A. C. Paley
  • Math . Z .
  • 1975

Similar Papers

Loading similar papers…