Paper Info
Title
2-Spreads and Transitive and Orthogonal 2-Parallelisms of PG(5, 2)
Abstract
A 2-spread is a set of two-dimensional subspaces of PG(d, q), which partition the point set. We establish that up to equivalence there exists only one 2-spread of PG(5, 2). The order of the automorphism group preserving it is 10584. A 2-parallelism is a partition of the set of two-dimensional subspaces by 2-spreads. There is a one-to-one correspondence between the 2-parallelisms of PG(5, 2) and the resolutions of the 2-(63,7,15) design of the points and two-dimensional subspaces. Sarmiento (Graphs and Combinatorics 18(3):621–632, 2002) has classified 2-parallelisms of PG(5, 2), which are invariant under a point transitive cyclic group of order 63. We classify 2-parallelisms with automorphisms of order 31. Among them there are 92 2-parallelisms with full automorphism group of order 155, which is transitive on their 2-spreads. Johnson and Montinaro (Results Math 52(1–2):75–89, 2008) point out that no transitive t-parallelisms of PG(d, q) have been constructed for t  1. The 92 transitive 2-parallelisms of PG(5, 2) are then the first known examples. We also check them for mutual orthogonality and present a set of ten mutually orthogonal resolutions of the geometric 2-(63,7,15) design.
Year
DOI
Venue
2010
10.1007/s00373-010-0943-8
Graphs and Combinatorics
Keywords
Field
DocType
full automorphism group,transitive t-parallelisms,two-dimensional subspaces,mutual orthogonality,known example,results math,orthogonal 2-parallelisms,point set,point transitive cyclic group,one-to-one correspondence,automorphism group,cyclic group
Discrete mathematics,Combinatorics,Cyclic group,Automorphism,Orthogonality,Linear subspace,Invariant (mathematics),Inner automorphism,Transitive closure,Mathematics,Transitive relation
Journal
Volume
Issue
ISSN
26
5
1435-5914
Citations 
PageRank 
References 
4
0.43
6
Authors
2
Name
Order
Citations
PageRank
Svetlana Topalova1258.30
Stela Zhelezova243.13