Resolutions of PG(5, 2) with point-cyclic automorphism group
✍ Scribed by Jumela Sarmiento
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 160 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1063-8539
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✦ Synopsis
A t-vY kY k design is a set of v points together with a collection of its k-subsets called blocks so that all subsets of t points are contained in exactly k blocks. The d-dimensional projective geometry over GFqY PGdY q, is a 2 À q d q dÀ1 Á Á Á q 1Y q 1Y 1 design when we take its points as the points of the design and its lines as the blocks of the design. A 2-vY kY 1 design is said to be resolvable if the blocks can be partitioned as R
, where s v À 1ak À 1 and each R i consists of vak disjoint blocks. If a resolvable design has an automorphism r which acts as a cycle of length v on the points and R r R, then the design is said to be point-cyclically resolvable. The design associated with PG(5, 2) is known to be resolvable and in this paper, it is shown to be point-cyclically resolvable by enumerating all inequivalent resolutions which are invariant under a cyclic automorphism group G hri where ' is a cycle of length 63. These resolutions are the only resolutions which admit a point-transitive automorphism group. Furthermore, some necessary conditions for the point-cyclic resolvability of 2-vY kY 1 designs are also given.