6533b7d6fe1ef96bd126714c
RESEARCH PRODUCT
On the type of partial t-spreads in finite projective spaces
Franco EugeniAlbrecht Beutelspachersubject
Discrete mathematicsCombinatoricsHyperplaneDimension (vector space)Projective spaceDiscrete Mathematics and CombinatoricsType (model theory)Element (category theory)Upper and lower boundsLinear subspaceSubspace topologyMathematicsTheoretical Computer Sciencedescription
AbstractA partial t-spread in a projective space P is a set of mutually skew t-dimensional subspaces of P. In this paper, we deal with the question, how many elements of a partial spread L can be contained in a given d-dimensional subspace of P. Our main results run as follows. If any d-dimensional subspace of P contains at least one element of L, then the dimension of P has the upper bound d−1+(d/t). The same conclusion holds, if no d-dimensional subspace contains precisely one element of L. If any d-dimensional subspace has the same number m>0 of elements of L, then L is necessarily a total t-spread. Finally, the ‘type’ of the so-called geometric t-spreads is determined explicitely.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1985-05-01 | Discrete Mathematics |