Recursive constructions for skew resolutions in affine geometries View Full Text


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Article Info

DATE

1981-12

AUTHORS

R. Fuji-Hara, S. A. Vanstone

ABSTRACT

A resolutionR inAG(n, q) is defined to be a partition of the lines into classesR1,R2, ...,Rt (t=(qn−1)/(q−1)) such that each point of the geometry is incident with precisely one line of each classRl, 1≤i≤t. Of course, the equivalence relation of parallelism defines a resolution in any affine geometry. A resolutionR is said to be a skew resolution provided noRi, 1≤i≤t, contains two parallel lines. Skew resolutions are useful for producing packings of lines in projective spaces and doubly resolvable block designs. Skew resolutions are known to exist inAG(n, q),n=2t−1,i≥2,q a prime power. The entire spectrum is unknown. In this paper, we give two recursive constructions for skew resolutions. These constructions produce skew resolutions inAG(n, q) for infinietly many new values ofn. More... »

PAGES

242-251

References to SciGraph publications

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URI

http://scigraph.springernature.com/pub.10.1007/bf02188038

DOI

http://dx.doi.org/10.1007/bf02188038

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1005070175


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