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Partitioning projective planes into arcs

Published online by Cambridge University Press:  24 October 2008

Barbu C. Kestenband
Barbu C. Kestenband
Affiliation:
Department of Mathematics, New York Institute of Technology, New York 11568, U.S.A.
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Extract

We show how to partition certain classes of finite projective planes into equicardinal arcs. Several partitions of this kind are to be found in the recent literature and they have aroused a certain amount of interest on two counts, as we shall shortly see.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 3 , November 1988 , pp. 435 - 440
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Boros, E. and Szönyi, T.. On the sharpness of a theorem of B. Segre. Combinatorica 6 (1986), 261–268.CrossRefGoogle Scholar
[2]Bose, R. C. and Chakravarti, I. M.. Hermitian varieties in a finite projeetive space PG(N, q 2). Canad. J. Math. 17 (1966), 1161–1182.CrossRefGoogle Scholar
[3]Ebert, G. R.. Partitioning projective geometries into CA's. Canad. J. Math. 37 (1985). 1163–1175.CrossRefGoogle Scholar
[4]Fisher, J. C., Hirschfeld, J. W. P. and Thas, J. A.. Complete arcs in planes of square order. Ann. Discrete Math. 30 (1986), 243–250.Google Scholar
[5]Hirschfeld, J. W. P.. Projective Geometries over Finite Fields (Clarendon Press, 1979).Google Scholar
[6]Hughes, D. R. and Piper, F. C.. Projective Planes (Springer-Verlag, 1973).Google Scholar
[7]Kestenband, B. C.. Projective geometries that are disjoint unions of caps. Canad. J. Math. 32 (1980), 1299–1305.CrossRefGoogle Scholar
[8]Kestenband, B. C.. A family of complete arcs in finite projective planes. Colloq. Math., (to appear).Google Scholar
[9]MacDuffee, J.. The Theory of Matrices (Chelsea, 1946).Google Scholar
[10]Thas, J. A.. Complete arcs and algebraic curves in PG(2, q). J. Algebra 106 (1987), 451–464.CrossRefGoogle Scholar