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Maximal Strictly Partial Spreads

  • Gary L. Ebert (a1)

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Let ∑ = PG(3, q) denote 3-dimensional projective space over GF(q). A partial spread of ∑ is a collection W of pairwise skew lines in ∑. W is said to be maximal if it is not properly contained in any other partial spread. If every point of ∑ is contained in some line of W, then W is called a spread. Since every spread of PG(3, q) consists of q2 + 1 lines, the deficiency of a partial spread W is defined to be the number d = q2 + 1 — |W|. A maximal partial spread of ∑ which is not a spread is called a maximal strictly partial spread (msp spread) of ∑.

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References

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1. Andrews, G. E., Number theory (W. Saunders, B. , Philadelphia, London, Toronto, 1971)
2. Bruck, R. H., Construction problems of finite projective planes, Combinatorial Mathematics and Its Applications, ed. Bose, R. C. and Dowling, T. A., The University of North Carolina Press, Chapel Hill (1969), 426–104.
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7. Orr, W. F., The miquelian inversive plane IP(q) and the associated projective planes, Dissertation, University of Wisconsin, Madison, Wisconsin, 1973.
8. Wilson, R. M., Cyclotomy and difference families in elementary abelian groups, J. Number Theory 4 (1972), 1747.
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Maximal Strictly Partial Spreads

  • Gary L. Ebert (a1)

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