Mathematics – Combinatorics
Scientific paper
2011-03-05
Mathematics
Combinatorics
This talk was presented at Matematiska kollokviet at Department of Mathematics at Link\"oping University on May 19, 2010
Scientific paper
A {\it vector space partition} is here a collection $\mathcal P$ of subspaces of a finite vector space $V(n,q)$, of dimension $n$ over a finite field with $q$ elements, with the property that every non zero vector is contained in a unique member of $\mathcal P$. Vector space partitions relates to finite projective planes, design theory and error correcting codes. In the first part of the talk I will discuss some relations between vector space partitions and other branches of mathematics. The other part of the talk contains a survey of known results on the type of a vector space partition, more precisely: the theorem of Beutelspacher and Heden on $\mathrm{T}$-partitions, rather recent results of El-Zanati et al. on the different types that appear in the spaces V(n,2), for $n\leq8$, a result of Heden and Lehmann on vector space partitions and maximal partial spreads including their new necessary condition for the existence of a vector space partition, and furthermore, I will give a theorem of Heden on the length of the tail of a vector space partition. Finally, I will also give a few historical remarks.
No associations
LandOfFree
A survey of the different types of vector space partitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A survey of the different types of vector space partitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A survey of the different types of vector space partitions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-8755